Baker signed a one-year contract to stay with the Astros after their World Series victory.
In his 25th season as a manager, the 73-year-old Baker earned his first World Series title when the Astros beat Philadelphia in six games.
The contracts of Click and Baker expired at the end of the season. Click said he was talking to Jim Crane about his future.
Jeff Luhnow and A.J. Hinch were both fired in the aftermath of Houston's sign-stealing scandal.
The COVID-19 season was shortened. The Astros made it to the playoffs as a wild card, but lost to the Dodgers in the NLCS.
The Astros won 95 games in 2021, and Baker made his first trip to the Series since 2002 with the San Francisco Giants, but the Astros fell to the Atlanta Braves in six games.
The Astros won 106 games this season, the second-best record in franchise history, and they won the World Series for the second time.