The meetings, which will take place at the team's Denver headquarters, could simply be an attempt by the Broncos to apply pressure on Elvis Dumervil, who was offered a contract Tuesday.
The Broncos also could be preparing to replace Dumervil if the defensive end decides to leave the franchise following last week's paperwork fiasco.
Broncos executive vice president of football operations John Elway acknowledged that the team submitted a contract proposal to Dumervil but declined to provide details.
Freeney, who played with Peyton Manning while becoming the Colts' career sack leader, is scheduled to fly to Denver on Wednesday night, according to league sources. Abraham will visit with the Broncos on Thursday, sources said.
Elway and other Broncos officials are traveling from Phoenix following the completion of the league's owners meetings.
A seven-time Pro Bowler, Freeney has 107.5 sacks over an 11-year career spent entirely with Indianapolis. But the 33-year-old Freeney struggled last season when he shifted from defensive end to outside linebacker in the Colts' 3-4 defensive scheme, recording just five sacks.
Freeney's 2012 statistics continued a steady decline over the past few seasons. In 2011, he had 19 tackles and 8.5 sacks, which were down from 25 tackles and 10 sacks in 2010. Those numbers were down from 2009, when Freeney had 31 tackles and 13.5 sacks.
Dumervil and the Broncos agreed upon a restructured contract that would have paid him $8 million in 2013. However, Dumervil's agent did not get the paperwork faxed to the team until seven minutes after the NFL deadline Friday. The Broncos were forced to cut Dumervil because they would have had to pay him $12 million in 2013 otherwise.
Dumervil fired agent Marty Magid on Saturday. The Broncos are open to re-signing Dumervil, and he reportedly wants to return. But there are salary-cap issues at play. Baltimore and Pittsburgh also have reportedly expressed interest in the 29-year-old pass-rusher.
He signed a six-year, $61.5 million contract in 2010 when Josh McDaniels was coaching the team and before Elway joined the Denver front office.
Dumervil had 11 sacks last season, second on the team behind Von Miller. Dumervil led the league with 17 sacks in 2009.
ESPN NFL Insider Adam Schefter and ESPN.com's Bill Williamson contributed to this report.