Reynolds, a junior, was OU's third-leading receiver last season, with 41 receptions, 715 yards and five touchdowns.
Franks was the Sooners' leading kick returner, averaging 23.9 yards a return as a sophomore last season, and caught 22 passes for 196 yards. Co-offensive coordinator Josh Heupel raved about Franks' all-around play during spring football.
Both Franks and Reynolds have been suspended before. Reynolds was suspended after tweeting insensitive comments about a gunman at the University of Texas during OU/Texas week, and redshirted that season. He was also suspended for one game last season for a violation of team rules.
Franks was suspended for two games last season for violating unspecified team rules.
Jackson started two games and played in 11 as a true freshman, finishing with 12 receptions for 165 yards. But he didn't participate in April's spring game.
News of Jackson's suspension comes just days after he tweeted he was transferring to Texas A&M. Reports in the aftermath of that announcement indicated the Aggies knew nothing of Jackson's plans to transfer.