According to an NFL source, multiple teams have expressed interest in signing the free agent, who is looking to shed the label of being strictly a special teams standout.
Graham would only be interested in returning to the Bears if the club offered significantly more money and afforded Graham the opportunity to compete for a starting job on defense, according to the source.
A 2007 fifth-round draft choice out of New Hampshire, Graham started nine games at cornerback in 2008 and recorded 93 tackles. Despite that output, he started only once the past two seasons, was passed over by Zack Bowman at cornerback in 2009 and lost a battle with D.J. Moore to be the Bears nickel back this past summer.
Graham, however, did develop into one of the Bears most valuable special teams players in 2010, and led the team with 25 special teams stops.
The Bears' top six special teams tacklers from last season are all free agents, and the club already lost Rashied Davis, who agreed to a one-year deal with the Detroit Lions.