HOUSTON — The Falcons had an important game on Sunday against the Saints. It helped determine the fate of their head coach, fired hours after the regular-season finale.

Washington and Michigan had an important game on Monday, to determine which is the best team in college football.

Three people set to play important roles Monday — Michigan coach Jim Harbaugh and quarterback JJ McCarthy, and Washington quarterback Michael Penix Jr. — didn’t want to talk about their futures this week before the College Football Playoff championship game. Those futures could be intertwined with the Falcons.

“There’s a calendar — I’ll gladly talk about the future next week,” Harbaugh said in preparation for the title game. “And I hope to have one, how about that? A future, I hope to have one, yes.”

Harbaugh, 60, has been linked to a return to NFL coaching. He led the 49ers from 2011-14. Michigan reportedly has offered to him a 10-year, $125 million contract extension. The NCAA is also investigating the Wolverines for numerous infractions.

Falcons owner Arthur Blank fired Arthur Smith on Sunday after he failed to lead the team to the playoffs in his three seasons.

Regardless of whether Harbaugh returns to the NFL and is a candidate to replace Smith, the Falcons are likely to look for a new quarterback, either in free agency or the draft. Penix and McCarthy are considered two very good prospects who may be available when the Falcons select. The Falcons have the eighth overall pick and may choose to move up in the draft to land one of the coveted quarterbacks.

Penix has passed for more than 4,600 yards in each of the past two seasons. A left-hander, he has a funky release but has completed an average of 63.6% of his attempts in four years at Indiana and two at Washington. A concern about Penix are the two ACL injuries, a broken clavicle and dislocated houlder injury he has sustained.

“I’m just super blessed to be in this position,” Penix said when asked about the NFL. “I really don’t focus in on the draft, stuff like that, because I feel like that God has a plan for me, and I’m going to trust that. For me, I’ve just got to go out there and fulfill his purpose, I feel like, and everything will work itself out.”

Penix has passed for 13,486 yards and 95 touchdowns with 32 interceptions. He has a fan in Harbaugh, who played quarterback at Michigan and described Penix as having “no conscience when he’s throwing,” and in McCarthy.

“He had my Heisman vote,” McCarthy said. “Michael Penix, everything he’s been through, all the adversity, all the injuries, just continuing to stick to the process and keep pressing on. ... He’s the epitome of that. The player he is, the touch he puts on the ball, the accuracy, the ball placement, just a tremendous quarterback and I have so much respect for him.”

McCarthy, a junior, was described by Harbaugh as the best quarterback in Michigan history. Better than himself. Better than Tom Brady. McCarthy is 26-1 as a starter and has passed for 6,086 yards with 49 touchdowns and 11 interceptions.

“I’s a tremendous honor,” McCarthy said. “Everything about Tom, like every aspect of his life, every aspect of his game, you want to aspire to be like it. Me personally, I don’t like comparisons because we’re unique and have different traits and aspects that makes us special. Just hearing that just gives you that reassurance that you’re on the right path and doing the right things. It means a lot, but at the end of the day I don’t like to compare myself to anyone. I just like to go out there and be the best version of myself.”