The Post's Mike Jones says Dan Snyder has decisions to make regarding Mike Shanahan's future, but Art Briles is not the answer. (Sarah Parnass/The Washington Post)

Mike Shanahan’s coaching tenure with the Washington Redskins appears closer than ever to ending. Members of the Redskins’ front office believe fractures in the relationship between Shanahan and team owner Daniel Snyder are now so deep that they are skeptical Shanahan can remain with the franchise beyond this season, several people familiar with the situation said Sunday.

Shanahan’s future was cast into doubt as the Redskins suffered a demoralizing, 45-10 loss to the Kansas City Chiefs on a cold and sloppy day before the smallest announced crowd since Fed Ex Field opened in 1997. Some fans threw snowballs toward the Redskins’ bench, and one was removed by stadium security personnel for screaming at Shanahan late in the game.

Most of the fans who did show up were long gone before the game ended, with the Redskins’ record dropping to 3-10 one year after they won the NFC East title.

“It’s embarrassing, depressing, everything,” tight end Niles Paul said in the team’s locker room afterward. “I’ve never seen fans just leave like that. I’ve never been a part of that. Get blown out like that, get embarrassed — that’s a tough pill to swallow.”

Snyder was not made available for comment, but according to people close to the team owner, Redskins management was angry over an ESPN report, published Sunday morning just hours before kickoff, that Shanahan had considered quitting after last season. The reason, the report said, was because he believed Snyder was too close to quarterback Robert Griffin III and that their friendship was damaging team morale.

Some Redskins officials questioned the timing and motivation behind those sentiments becoming public, the people with knowledge of the situation said, with some suggesting Shanahan — or someone close to him — was behind the story. The Redskins officials, who spoke on condition of anonymity because of the sensitivity of the situation, said a parting of the ways between the team and Shanahan was increasingly likely.

“I don’t know that it can be fixed now,” one said.

Shanahan declined to address his future or relationship with Snyder during his postgame news conference. “It’s not the right time or place to talk about my relationship with Dan Snyder,” Shanahan said. “Or it’s not the right time and place to talk about something that happened a year ago. I’ll get a chance to talk to Dan at the end of the season. I’ll give some viewpoints from me, and I’m sure he’ll give me his thoughts on what direction we’ll go. And so we’ll communicate that at the proper time.”

Snyder fired a coach once during a season, dismissing Norv Turner with three games remaining in the 2000 season and replacing him with interim coach Terry Robiskie. Snyder has said since that firing Turner during the season was a mistake.

The Redskins’ latest defeat came on a bleak, gray day in Landover. Snow turned to sleet and freezing rain as the afternoon progressed. Many seats at FedEx Field were not filled at kickoff, and the stands steadily emptied even further as the Redskins fell behind by 31-0 in the second quarter and 38-10 at halftime.

Redskins players did not mince words describing their play. Tight end Logan Paulsen said the team suffered from “a full community offensively of deficiency.” Linebacker Ryan Kerrigan said the Redskins “didn’t stop anybody defensively.” Paul said the special teams were “terrible.” Asked what had gone wrong, wide receiver Pierre Garcon said: “Everything.”

Veteran linebacker London Fletcher was asked whether some Redskins players had quit. “Prior to coming to this game, I would have said that’s not the kind of character [of] the locker room we have. But then when you see this type of performance . . . where you give up as many yards as you give up from a special teams standpoint or not being able to move the ball offensively and not being able to tackle defensively, it’s hard to say what it was. But it wasn’t a good sight. The fans weren’t booing for no reason.”

Shanahan removed Griffin from the game and went to second-year backup Kirk Cousins early in the fourth quarter with the Redskins trailing 45-10. Only a few thousand fans remained in the stands at that point.

“I take full responsibility for this game today,” Shanahan said. “I didn’t have our players ready to play. I thought they were ready to play. We did obviously horrendous on special teams, giving up big play after big play. We didn’t tackle like we normally tackle on defense. Offensively we did a couple good things [but] couldn’t get anything going in the second half. So I’ll put that all on me.”

Shanahan refused to say whether he had spoken Sunday to Snyder and declined to answer a question about whether he wanted to remain the team’s coach.

“There’s only one focus I have now,” he said. “Any time that you’re 3-9 or 3-10, there’s gonna be constantly things brought up time after time. . . . So I’m not gonna go down that road, because I understand what happens when you’re having the type of season that we’re having.”

Shanahan got into back seat of a black SUV and left the stadium around 5:20 p.m.

Multiple people with knowledge of the thinking of Redskins officials said members of the team’s management wonder whether Shanahan hopes to leave the organization so he can be a candidate for the Houston Texans’ coaching vacancy.

Texans owner Robert McNair fired Gary Kubiak as that team’s coach Friday, with the Texans on an 11-game losing streak that has dropped their record to 2-11. The Texans could have the top overall selection in the NFL draft this spring, and the job still is regarded as attractive to those within the industry. Shanahan’s son, Redskins offensive coordinator Kyle Shanahan, had the same job with the Texans and could accompany his father to Houston.

Shanahan is in the fourth season of a five-year contract with the Redskins that pays him approximately $7 million per season. He has a regular season record of 24-37 with the team.

The ESPN report said Shanahan cleaned out his office before the Redskins’ playoff loss to the Seattle Seahawks last January in preparation of quitting but changed his mind after Griffin reinjured his right knee during that game, necessitating surgery days later.

People who were in Shanahan’s office in the days immediately before and after the Seattle playoff game said they did not notice the office being cleared out.

One person with close ties to the Redskins organization said Shanahan did contemplate quitting after last season. That person did not specify whether Shanahan went so far as to clean out his office and did not say how close Shanahan came to actually quitting.

It is believed Shanahan would be owed the remainder of his contract if he is fired but would not be owed that money if he quits. It is not clear whether the Redskins, under the terms of Shanahan’s contract, could prevent him from coaching elsewhere next season if he resigns. It is also not known whether any money Shanahan makes from a different team next season, if indeed he exits and lands another coaching job, would be subtracted from the amount the Redskins owe him.

A person with knowledge of the relationship between Snyder and Shanahan said there was no sign of friction between Shanahan and Snyder at the end of last season. According to that person, Snyder has attempted to meet all of the requests made by Shanahan during his coaching tenure by moving the Redskins’ training camp to Richmond, building an indoor practice facility at Redskins Park, hiring a new chef to cook meals for players and coaches at the club’s headquarters and upgrading the team’s travel accommodations during road trips.

That person said Griffin’s wife, Rebecca, expressed disappointment to the team about being mentioned in the ESPN report, which said she was spotted being picked up by Snyder’s driver at road games. She told a team official she takes taxicabs to games, that person said.

Jason Reid and Mike Jones contributed to this report.