The 66-year-old star - who has been fronting 'The Late Show with David Letterman' for 32 years - wants to rebuild relations with the former 'The Tonight Show' host who he famously fell out with.
Show producers have had the idea in the works for a while but wanted to wait until former 'Saturday Night Live' star Jimmy Fallon - who replaced Jay as show host - made his debut on 'The Tonight Show' on February 17.
A source told New York Daily News' newspaper column Confidenti@l: "There's been quiet talk behind the scenes for months that Dave will have Jay Leno on as a guest.
"(Letterman's) producers waited until Fallon debuted (on 'Tonight'), give him space out of respect, but are now ready to pull out all the stops."
Jay and David were good friends but are said to have had a dispute after the 63-year-old presenter landed a spot on popular 'The Tonight Show' in 1992, when he replaced Johnny Carson as host, but many expected David to be Johnny's successor.
They reportedly had a 20 minute phone chat to smooth over any bad feelings.