Elvis Dumervil doesn’t want this to be about money.

An NFL source familiar with the Dumervil free-agent proceedings said the pass rusher’s primary consideration in picking between the Broncos, the Baltimore Ravens and possibly another team or two: He wants to feel wanted.

And what Dumervil has been trying to wrestle with in recent days is the fact that the Broncos cut him, even though there may have been a series of bizarre events that led to his release.

Regardless of what led to it, in Dumervil’s mind, the Broncos cut him. Peyton Manning had the same feelings last year with the Indianapolis Colts. It may have been a no-brainer decision for the Colts to release Manning in lieu of paying him $35 million after he missed an entire season because of four neck surgeries — while at the same time, Indianapolis had a ready, younger replacement in Andrew Luck available with the No. 1 draft pick.

It still took Manning a few days to deal with the fact he essentially was fired.

Dumervil is experiencing similar feelings. That’s not to say he won’t choose to re-sign with the Broncos, the only team he has played for in his seven-year NFL career. But the source said Dumervil wanted to pray and sleep on his decision Friday night.

The Dumervil saga has been the most protracted, twisted contract saga in Broncos history. So what’s another day?

It started a month ago when the Broncos sought to reduce Dumervil’s $12 million salary in 2013. After some bargaining tussles, both sides agreed on a reduction to $8 million in 2013 — only to have the revised paperwork not get transmitted in time to beat a 2 p.m. March 15 deadline to NFL headquarters in New York.

The Broncos then released Dumervil, a three-time Pro Bowler, to free agency by terminating his original contract to avoid guaranteeing the $12 million salary.

After spending a week in free agency, Dumervil received offers from the Broncos and the Super Bowl champion Ravens.

If it was about money, the source said, Dumervil already would have re-signed with the Broncos because through most of the week in which he has been a free agent, his former team still had the best offer on the table.

The Ravens have since come close to matching the Broncos’ three-year offer, according to an NFL source. Dumervil’s camp has said at least one more team is involved in discussions.

If Dumervil decides against re-signing with the Broncos, they are prepared to sign one of two veteran defensive ends — John Abraham or Dwight Freeney.

Meanwhile, another former Broncos defensive player who was released to free agency this month, longtime starting linebacker D.J. Williams, signed a one-year contract with the Chicago Bears. Williams is expected to replace Brian Urlacher at middle linebacker.

Urlacher approached superstar status during his career with the Bears, but they released him Thursday.

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