When the season had finally ended, Rex Grossman was the first player off the field, sprinting into the stadium tunnel for a final time. Later, his hair still damp from a postgame shower, Grossman walked out of the Washington Redskins’ locker room wearing a blue pinstripe suit and pulling a roller bag behind him.

First stop, the team bus. Then on Monday morning, Redskins Park to pack up his locker. And after that — who knows? Grossman will be a free agent, and the future of the Redskins’ quarterback position is up in the air.

As the Redskins begin to weigh their options, though, Grossman said he’d like to return to Washington next season.

“I really enjoy it here. I really enjoy this offensive system, what they’re building here,” he said following the Redskins’ 34-10 loss to the Eagles on Sunday. “So I’d love for this to be the place where I end up.”

Of course, that decision will ultimately be made by Coach Mike Shanahan and his staff, not the nine-year veteran quarterback. Shanahan in recent weeks has said the team’s turnover problems this season were unacceptable. In 13 starts, Grossman had 20 interceptions and five lost fumbles.

Shanahan already has started evaluating the quarterbacks who will be available in this year’s NFL draft. Before that, though, the team will have to make a decision on Grossman — and all of the other free agent quarterbacks, including Green Bay’s Matt Flynn, who raised some eyebrows Sunday with his six-touchdown, 480-yard performance.

Grossman’s agent, Drew Rosenhaus, attended the Redskins’ game Sunday at Lincoln Financial Field and said it’s too early to guess what Grossman might do in free agency.

“I don’t really want to speculate what might happen right after a loss like this,” he said.

After beating out John Beck in a preseason position battle, Grossman started 13 of the Redskins’ 16 games. He threw at least one interception in each but also threw for at least 250 yards seven times. In Sunday’s season finale, he was 22-for-45 passing for 256 yards with one touchdown and one interception.

That lone interception Sunday was the product of a broken play, resulting in a severely underthrown pass to Anthony Armstrong. Still, it was the type of play that highlighted one of Grossman’s biggest strengths — his fearlessness in heaving the ball downfield — and biggest drawbacks — the tendency for the other team to make the catch.

“Houdini couldn’t have thrown the football in that,” Shanahan said. “But Rex threw the ball up in the air, gave [Armstrong] a chance to make a play.

“Rex played a heck of a ballgame today,” the coach continued. “To have that type of pass rush and make some of the throws that he did under duress, I don’t have a problem with the way he played.”

Even though Shanahan benched Grossman in favor of Beck for a three-game stretch, the coach said Grossman made strides from Week 1 to Week 17.

“I think Rex feels a lot more comfortable with the system. The more reps you get, the better off you feel,” Shanahan said. “You can see over the last four or five games, he’s felt a lot more comfortable.”

The season might have had more lows than highs — Grossman predicted a division title for a team that won only five games — but the veteran quarterback said he’ll look back on the year and note the positives. “There’s a lot of good things,” he said.

Despite missing three games, Grossman finished the season with 3,151 passing yards, just 42 yards shy of his career high, set in Chicago in 2006. His 20 interceptions matched his career high, also set in 2006.

He was a free agent each of the past three years, signing a one-year contract with the Redskins the past two. So Grossman is certainly familiar with offseason uncertainty.

“It’s part of this job. . . . Obviously, everybody would love to have a 10-year contract worth $200 million and you could just Albert Pujols it,” he said. “That’s not always the case and you just got to work hard and go about it, worry about what you can control and take care of business.”

The free agent market for quarterbacks is not expected to be a deep one, and with Grossman having spent three years in this system — he was Houston’s backup quarterback in 2009 under offensive coordinator Kyle Shanahan — it’s possible Washington might still represent his best opportunity to contribute to an NFL team next year.

“I’m not sure what my opportunities are going to be. But I hope this is the best opportunity,” he said. “And like I said, it’s a very good team, I’m proud of every single teammate that I played with.”