Keith McMillan explains what the creative play-caller will bring to Washington. (Jayne Orenstein/The Washington Post)

Jay Gruden began settling in and addressing a lengthy to-do list Friday on his first full day as coach of the Washington Redskins.

Members of the organization said that Gruden, the former offensive coordinator of the Cincinnati Bengals hired Thursday by the Redskins to replace the fired Mike Shanahan, had a hectic day as he scurried busily from office to office at Redskins Park. One of Gruden’s first tasks is to fill out his coaching staff.

Several people with ties to the team continued to say Friday that holdover assistant coaches Jim Haslett, Raheem Morris and Sean McVay are expected to remain on Gruden’s staff. Gruden did not commit to that Thursday, saying he knows there are good coaches within the organization but he also believes there are good coaches elsewhere and he wants to interview a variety of candidates.

Haslett, Morris and McVay worked for Shanahan but were not fired by the team when Shanahan and much of his staff were dismissed. Haslett was the team’s defensive coordinator under Shanahan. Morris served as the secondary coach, and McVay was the tight ends coach. All also have ties to Gruden. McVay and Morris worked with him with the Tampa Bay Buccaneers. Haslett and McVay worked with him in the United Football League.

People with knowledge of the team’s planning said Friday that McVay remains in line to be promoted to offensive coordinator, while Haslett and Morris are likely to retain the roles they had overseeing the team’s defense. That does not, however, preclude a reshuffling of titles, and Morris perhaps could be given some added responsibilities.

Gruden was not available to comment Friday.

Backup quarterback Kirk Cousins said Friday that McVay would be a valuable asset in an expanded role.

“I think the positives with Sean as an offensive coordinator, aside from the fact that it’s going to be continuity — from my standpoint, two years’ worth of understanding of what I can do and even more so with other players — is Sean is extremely positive, and players in general have a good relationship with him, enjoy playing for him and speak well of him,” Cousins said. “He’s very, very intelligent. Sometimes I have to say to Sean, ‘Slow down and put that in my terms,’ because he knows football so well that he can talk football as well with anyone. So I think his energy, how positive he is and the fact that he’s so intelligent, I think it’s going to be a great opportunity for him and the beginning of a very, very good career.”

Cousins said he was encouraged by the selection of Gruden as the team’s coach.

“It’s nice that the head coach has played quarterback and understands the quarterback position, and personally, I think that’s a good thing for us quarterbacks,” he said.

Cousins started the final three games of the 2013 season. But Gruden said Thursday that Robert Griffin III, who was shut down by Shanahan for those three games, remains the unquestioned starter. It remains to be seen whether the Redskins will keep Cousins or trade him to a quarterback-needy team this offseason. For now, Cousins is preparing as if he will remain with the team that drafted him in the fourth round out of Michigan State in 2012.

Gruden spent the past three seasons guiding the Cincinnati offense. He, like Mike Shanahan and former Redskins offensive coordinator Kyle Shanahan, is an extension of Bill Walsh’s West Coast offense coaching family. Cousins said that based on his observations of the Bengals’ offense run by quarterback Andy Dalton, a number of similarities exist and that could make for a smoother transition.

“I always felt like it was good to watch our opponents versus Cincinnati because through a formations and pass concepts standpoint and even from the type of quarterback that Andy is, I felt like it always gave me a good look of what I would see if I were to play on game days,” Cousins said. “My experience with their offense has been watching it on film and studying the defense they’ve played. For example, we played Chicago this year. I watched a lot of Cincinnati film against Chicago. Obviously the first thing that stands out to you is the number of weapons they have to get the ball to. But certainly I always felt like if I were to pick a team in the league that most closely resembled what we did, I would personally say that Cincinnati is right up there with anybody.”

Many of the team’s skill-position players share Cousins’s sentiments. Wide receiver Pierre Garcon also expects a smooth transition and improvement by the offense.

“Man, I am real excited about Coach Gruden and what he brings to the Redskins and our quest for a Super Bowl,” Garcon said.

Gruden’s body of work also impressed members of the defense. In their meeting during the 2012 season, the Bengals’ offense racked up 478 yards in a 38-31 victory. On the first play of the game, wide receiver Mohamed Sanu lined up in the Wildcat formation and torched Washington’s defensive backs for a 73-yard touchdown pass to A.J. Green. Quarterback Andy Dalton went on to pass for 328 yards and three touchdowns.

“I know having played the Bengals last year and having seen them the last couple years with him as the leader of their offense, they’ve been one of the better offenses in the league,” outside linebacker Ryan Kerrigan said. “That’s exciting having someone of that mind coming to your team and leading your coaching staff.”

Meanwhile, the news that Haslett would remain as defensive coordinator and that the Redskins will continue to run a 3-4 defensive front was a welcome development, said Kerrigan, who at the conclusion of the season had worried about the hindrance of development that a new coaching staff could cause.

“I liked it. Haz and a lot of the guys on the team — myself included — all have a great relationship. He’s someone that we want to play hard for. He’s a great coach. and he’s fun to play for,” Kerrigan said. “This is a defense that, especially as an outside linebacker in the defense, takes a while to really get comfortable in. So to continue to play in the same style of defense and for the same coach is pretty nice.”