According to the New York Times, NBC has "made a commitment" to Fallon, who currently hosts the network's "Late Night With Jimmy Fallon," airing after Leno. (The TImes says, however, that a deal has not yet been struck.)
Also read: Leno Jokes NBC Execs are 'Snakes' (Video)
The Times says that NBC is also building a studio in the network's New York headquarters at 30 Rockefeller Plaza to accommodate the switch in hosts. (Fallon currently tapes "Late Night" in New York; "Tonight" was originally filmed in New York, before moving to Burbank, Calif., in 1972.)
As for when Fallon would assume Leno's duties, the Times reports that the transition is slated for a fall 2014 timetable, when Leno's contract expires.
A spokeswoman for NBC has not yet responded to TheWrap's request for comment.
Leno took a couple of pointed jabs at NBC brass on his show this week, after a report that he and NBC entertainment chairman Robert Greenblatt had an argument over Leno's previous "Tonight Show" digs about the network's ratings.
"Well you know the whole legend of St. Patrick, right?" Leno cracked during his monolog on Monday night's show. "St. Patrick drove all the snakes out of Ireland, and then they came here to the United States and became NBC executives. It's a fascinating, fascinating story."
Tuesday night found Leno landing another shot at NBC's expense, over — uh-huh — the network's ratings.
"Did you hear about this? A 28-year-old woman from Serbia has a rare brain condition where she sees everything upside down," Leno joked. "The good news? She's now been given a job at the White House as President Obama's economic adviser. Isn't that crazy? It's unbelievable. She sees everything upside down. In fact, she thinks NBC is at the top of the ratings."