But Leiweke, president of Galaxy owners AEG, refused to confirm they had made a move for the Chelsea midfielder.
Leiweke confirmed that Galaxy were looking at their options for future Designated Player slots.
In Major League Soccer, clubs can sign up to three Designated Players which are not included in the otherwise strict wage structure that operates throughout American football.
"I am a fan of Frank's, I think he is a great player. When I think of Chelsea, I think of Frank Lampard," Leiweke told Sky Sports News.
"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 backed Lampard's link with the Galaxy, adding: "If he does decide to walk away from Chelsea, then of course which team would not want him?
"The owners are very persuasive, so of course there is a chance."