In addition to speaking with Forte's representatives during the NFL combine, a development first reported by the NFL Network, the Bears also have conducted meetings from a suite at the Hyatt Regency in downtown Indianapolis with reps for some of the team's pending free agents.
Phil Emery assumed the GM post this offseason after Jerry Angelo was fired.
The previous offer to Forte amounted to between $13 and 14 million in guaranteed money, a source told ESPNChicago.com, and talks broke down just before the start of last season, when the 26-year-old running back declined to accept the first and only deal extended by the club.
Given Forte's age, it's believed the team was looking to sign him to a five-year deal.
Forte enters his fifth year this fall, and there's sufficient evidence to suggest the Bears wouldn't be making a mistake by signing him to a long-term deal. The common perception is that a running back's production tapers off after four years, but according to ESPN Stats & Information, that's not always the case.
Focusing on players who were well-established before their fifth season, ESPN Stats & Information examined a handful of notable running backs who played seasons 5 though 7 since 2000.
Only two -- Shaun Alexander and Corey Dillon -- did not rush for more than 1,200 yards in their seventh season. Two others -- Fred Taylor and Edgerrin James -- enjoyed multiple 1,000-yard seasons after Year 7. Dillon's best season didn't come until Year 8 (career highs with 345 rushes for 1,635 yards).
Peterson, Johnson and Jackson were 1-2-3 in average salary for running backs last season, with Jones-Drew sixth. Charles was ninth and Gore 13th.
Forte was named to his first Pro Bowl in 2011 after he led the team with 1,487 yards from scrimmage despite missing the final four games after suffering a sprained medial collateral ligament in his right knee during a Dec. 4 loss to the Kansas City Chiefs.
Bears coach Lovie Smith said Thursday that he believes Forte will be playing for the Bears for a long time.
"Matt is going to play his football for the Chicago Bears, you start with that," Smith said at the NFL scouting combine. "In time, hopefully we can get an agreement in place that suits Matt and we feel comfortable with. I think it's just a matter of time. That will happen eventually."
If it doesn't, the Bears own the option of designating Forte their franchise player before the March 5 deadline.
With the tag, Forte would receive a one-year deal worth a projected $7.7 million.
Michael C. Wright covers the Bears for ESPNChicago.com and ESPN 1000. Information from ESPNChicago.com's Jeff Dickerson was used in this report.