The future of the England international has been called into question in recent weeks following reports that the 33-year-old was frustrated at the lack of first-team football at Stamford Bridge.
"I am a fan of Frank's, I think he is a great player," Leiweke told Sky Sports News. "When I think of Chelsea, I think of Frank Lampard. You should ask him, it took us two years to get David here the first time, we are working on the next DP.
"We are going to continue to work on the next DP and there are about half a dozen guys we have a good relationship with, but first we have to have a lot and we don't have a slot. I am a big fan of his."
Beckham claimed that the LA Galaxy owners can be "very persuasive" when asked whether Lampard could have a future in America.