As Dwight Freeney and John Abraham took turns visiting Thursday with the Broncos at Dove Valley, the Baltimore Ravens made a strong push for Elvis Dumervil.

Perhaps this dragged-out Dumervil pay-cut saga is nearing its end.

The Ravens have delivered a contract offer to Dumervil, according to two NFL sources. However, the sources say the Broncos have offered slightly more money in the early portion of the deal.

The Broncos’ money has tightened because of a $4.89 million dead-money, salary cap hit they absorbed while releasing Dumervil last week, so re-signing the defensive end likely would mean releasing a player or two off their roster.

The Miami Dolphins and Tennessee Titans are talking with Dumervil’s agent, Tom Condon, but have not made formal offers, according to the two sources.

Dumervil, 29, had been with the Broncos since he was one of their fourth-round draft choices in 2006. He missed the 2010 season because of an injury but had 63½ sacks in his other six, an average of 10.6 sacks per year. He has been named to three Pro Bowl teams.

“There will be a plan in place and John Elway will execute it,” Broncos president Joe Ellis said Wednesday as he was leaving the NFL owners meetings in Phoenix. “It would be great to see Elvis come back. He’s been a great player for the Broncos. Time will tell.”

After the Broncos paid Dumervil $14 million in 2011 and another $14 million in 2012, Elway, the Broncos’ front-office boss, and Mike Sullivan, the team’s contract negotiator and salary cap manager, informed Dumervil’s agent, Marty Magid, at the NFL scouting combine last month they did not want to pay his client another $12 million in 2013.

After acrimonious and protracted negotiations, a revision to the final three years of Dumervil’s contract was orally agreed upon last Friday. The $30 million sum of the contract remained, although his 2013 salary was reduced from $12 million to $8 million.

However, when the signature page of the revised contract did not make it from a fax machine at a Kinko’s in Miami to the Broncos’ offices in time for the Broncos to send off the final paperwork to the NFL office in New York by 2 p.m., the revised deal never was executed.

Instead, minutes before that deadline, the Broncos terminated his original contract and Dumervil became a free agent.

Once he hit the market, there was immediate mutual interest between Dumervil and the Ravens. The connection is Baltimore linebackers coach Don “Wink” Martindale, who was the Broncos’ linebackers coach in 2009 when Dumervil posted his career-best 17 sacks.

That season, the Broncos were using a three down linemen-four linebackers system where Dumervil was moved from defensive end to outside linebacker for the first time in his career. The Ravens, who won the Super Bowl last month, use a similar 3-4 defensive system.

Before the Ravens entered negotiations with Dumervil, the Broncos had submitted a new three-year offer Monday night. Dumervil’s camp, though, was not happy with the discounted salary in the second year of the Broncos’ proposal. If the Broncos and Dumervil finally part ways, Denver is expected to sign Freeney or Abraham.

Freeney, 33, played his first 11 seasons with the Indianapolis Colts. He had only five sacks last season. Abraham, who will soon turn 35, played six seasons with the New York Jets and the past seven with the Atlanta Falcons. He had 10 sacks last year.

Both Freeney and Abraham, though, are speed rushers who are leaving teams that played indoors on an artificial surface. The Broncos play outside and on grass at Sports Authority Field at Mile High.

Mike Klis: 303-954-1055, mklis@denverpost.com or twitter.com/mikeklis