Sources told ESPN.com that Edgar was offered the title shot Monday night.
Edgar (11-1-0) has won three fights in a row. In his most recent bout, he submitted Matt Veach in the second round at "The Ultimate Fighter 10 Finale."
During the victory, Edgar displayed improved stand-up skills. That performance secured the bout with Penn (15-5-1).
"He has a real fast pace," UFC CEO Lorenzo Fertitta told ESPN.com. "He's got good boxing skills, and he is a real tough guy.
"We think it is the most compelling matchup that can be made right now."
While serious negotiations for Penn-Edgar have yet to begin, no one foresees any difficulty making the fight a reality. Penn recently expressed a desire to defend his 155-pound title April 10 at UFC 112 in Abu Dhabi.
The chances of Maynard, who has a win over Edgar, being Penn's next opponent evaporated during his struggles with Diaz. Each of Maynard's past six fights has gone the distance and none was an eye-opener.
His two most recent wins, against Diaz and Roger Huerta (at UFC Fight Night 19 in September 2009), were by split decision. Maynard's less-than-stellar victories may have delayed his title shot, but not his standing in the division
"He's right at the top. He's absolutely right at the top," Fertitta said. "He needs a fight or so under his belt; he's done a great job.
"He won a decision against a very tough guy last night. He's right in line."
As for why Edgar got the nod over Maynard, Fertitta got right to the point.
"Like I said, [Maynard] is certainly up there at the top. But right now, we want to put on fights that we feel will sell the best. Right now, we think that's Frankie Edgar, based on the fight that we saw last night."
Franklin McNeil appears regularly on ESPN.com's "MMA Live."