Mariota, who is 23, officially is considered day-to-day with a hamstring injury sustained during Sunday's 57-14 loss at Houston.
Mularkey says a final decision on whether Mariota plays when Tennessee visits Miami (1-2) could come just before the game Sunday.
Backup quarterback Matt Cassel relieved Mariota on Sunday, and is expected to start of Mariota is unable to play.
Weeden, seen above getting sacked by the American flag, started 20 games for the Browns in 2012 and 2013, eventually losing the starting role to Jason Campbell. The 6-foot-3 Weeden has thrown for 6,452 yards with 31 touchdowns and 30 interceptions.