The controversy was first ignited by jokes Leno made about NBC's February sweeps ratings, which caused NBC Entertainment Chairman Robert Greenblatt to take offense.
Since the dust-up, rumors have been swirling that NBC has debated speeding up the timing of Leno's contract, which expires September 2014. Some top NBC executives would like Jimmy Fallon to take over as host of the "Tonight Show" in February 2014 to coincide with the airing of the Winter Olympics in Sochi, Russia, The Hollywood Reporter said.
In reaction to the rumors, Leno has been making more jokes about the network during his opening monologues, the report said.
On Friday he told the news report of Canadian doctors who removed a knife from the back of a man after it had been lodged there for three years.
"Imagine that. The guy had a knife in his back for three years. He must have worked at NBC too," Leno said.
He continued by making a joke about a Carnival cruise that had recently gone awry.
"Have you heard about this alleged feud that I'm having with NBC? I think it's going to be OK," Leno said. "This is real. I had dinner last night with a bunch of executives. To make it up me, what they did, they are sending my wife and I on an all-expenses-paid Carnival cruise."
"So it looks like it's going to be OK. Fantastic!" he added.
Celebrity Families of 2014 [PHOTOS]