Over the course of eight NFL seasons with three teams, Griese has passed for 16,344 yards with 103 touchdowns and 78 interceptions. The 31-year-old has started 72 of 75 games.
While the Bengals are the only other team Griese has met with, the Ravens and Raiders are also said to have interest in the six-foot-3, 214-pounder.
Last year, Tampa Bay got off to a 5-1 start with Griese under center, but a torn ACL and MCL suffered on Oct. 16 ended his season. Although Tampa Bay cut him before having to pay a $2.6 million bonus, there is a chance the Buccaneers could also come back into the picture.
If Griese lands in Chicago, he would push Kyle Orton to third on the depth chart.
The Philadelphia Eagles released QB Mike McMahon on Monday. The recent addition of Jeff Garcia cleared the way for the move. McMahon started seven games last season after Donovan McNabb went down with an injury.
The Clock is Ticking
The Bears have until midnight on Friday to decide whether or not to match the offer sheet restricted free agent DL Israel Idonije signed with the Buffalo Bills. The deal is worth $8.2 million over four years, including a $1.8 million signing bonus.
If the Chicago declines to match the offer, the team will not receive any form of compensation.
Tight end Jeb Putzier's has agreed to a four-year $7.5 million contract with the Houston Texans on Monday which includes a $1.85 million signing bonus.
The Bears never had anything more than passing interest in Putzier, who caught 73 passes over the last two seasons for the Denver Broncos. After re-signing reserve TE John Gilmore, Chicago is likely to address the position on the first day of the draft.
Tucker came into the league as a third round pick in 1999. He spent his first six seasons with the Bears and was a Pro Bowl alternate at guard in 2001. Injuries limited his playing time from 2002-04. The Bears finally cut ties with Tucker last year and he landed with the St. Louis Rams, where he played for Lions offensive coordinator Mike Martz who was the Rams coach at the time.