The former Manchester United star is set to make his final appearance for the Galaxy in the 2012 MLS Cup decider with Houston Dynamo on the weekend, ending six years as a player with the reigning North American champions.
Galaxy chief executive Leiweke spoke of the brilliant relationship the franchise has had with Beckham and admitted that he would like to see the 37-year old back in Carson, California, quite possibly as part-owner.
"I think the gas and speculation is pretty good. David and this franchise and this ownership group have had a great relationship," said Leiweke.
"I don't think it's going to end here but we'll wait until the right time. We're focused on the cup final on Saturday and playing that. We'll get through the game on Saturday and deal with that later.
"David and us started this vision together. We spent two years talking to him, getting him comfortable and working through how to get him here. He has then spent six years here.
"When you look at all of that, the relationship and the longevity, we've been partners for eight years and that doesn't end so quickly or so easily.
"If there are ways to ultimately continue to develop that relationship to grow the sport and for him to stay part of the Galaxy, we've always said we want to be in the relationship forever, not for six years."