The 33-year-old has fallen down the Stamford Bridge pecking order since the summer arrival of Blues boss Andre Villas-Boas, leading to speculation that Lampard could join the likes of David Beckham, Thierry Henry and Robbie Keane in North America.
In an interview with Sky Sports News, the president of LA Galaxy owners AEG, refused to confirm that the club had approached Chelsea about the possibility of signing him this month.
"I am a fan of Frank's, I think he is a great player. When I think of Chelsea, I think of Frank Lampard," said Leiweke. "You should ask him, it took us two years to get David [Beckham] here the first time, we are working on the next designated player.
"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."
In Major League Soccer, clubs can sign up to three 'designated players' which are not included in the strict wage structure that operates throughout American football.
Beckham, Keane, and Everton loanee Landon Donovan are Galaxy's three current DPs for the new season set to start in March, but that doesn't mean that Lampard could ply his trade in Los Angeles in the future.
"If he does decide to walk away from Chelsea, then of course which team would not want him," questioned Beckham. "The owners are very persuasive, so of course there is a chance."