Glennon, 27, however, wants to be a starting QB and plans to test free agency, according to Caplan.
The Tampa Bay Times first reported the contract offer.
The Bucs' offer to Glennon would eclipse the deal that the Eagles gave QB Chase Daniel ($7 million per season).
Glennon has seen action in 21 career games with 18 starts for the Bucs, although he hasn't started a game in the past two seasons.
Purely a drop-back passer, Glennon has a strong arm that will function in an offense designed to push the ball downfield, which worked perfectly for Greg Schiano's offense under Mike Sullivan but wasn't ideal when Jeff Tedford became offensive coordinator for the Bucs. West Coast systems relying on shorter, quick throws aren't his forte, and he does not offer much in the way of mobility.
In 2013, his rookie season, Glennon started 13 games and threw for 19 touchdowns and nine interceptions. He threw for 2,608 yards that year while completing 59 percent of his passes.
In 2014, he started five games for Josh McCown, completing 57.6 percent of his passes for 1,417 yards, 10 touchdowns and six interceptions. He has 30 career touchdown passes, 15 interceptions and a passer rating of 84.6.
ESPN's Jenna Laine contributed to this report.