It would need a considerable offer to prise Lampard, 33, from Stamford Bridge, especially since his sparkling form has silenced doubts over his future under new manager Andre Villas-Boas.
But Galaxy need to find someone closeto Beckham's profile if speculation about him leaving the Home Depot Center after next Sunday's sell-out MLS Cup final against Dynamo Houstonturns out to be well founded.
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? Beckham is undecided about whether to stay with Galaxy or take up one of the options available to him in England and Italy, while the offer to join Paris Saint-Germain, backed by Qatar's billions and led by director of football Leonardo, his former colleague at AC Milan, is proving difficult to resist.
He intends to explore every avenue before making his choice.
In spite of the popular belief that Beckham, 36, was committing professional suicide by quitting Real Madrid for the then little-known American club, his five years at Galaxy have been a success, for him personally and professionally, and especially for the club, whom he has put on the world football map.
Such has been his impact in Los Angeles that they would move heaven and earth to persuade him to sign another deal.
Delivered: Beckham is popular in the States
MLS commissioner Don Garber said: 'David has delivered for us on all aspects of our expectations, both on and off the field.
'David had a terrific year this year. It would be hard to argue he wasn't one of the most important players on our fields.
'Off the field, he continues to be an important part of what drives some of the popularity of our league, both here and around the world.
'He remains a very popular guy. His presence on the sports pages but also on the "people pages" continues to grow here in America, and we benefit from that.
'MLS wouldn't be what it is today if David didn't come to play in Major League Soccer. All of us appreciate everything that he has done.
Instant hit: Robbie Keane (left) has joined Beckham (centre) in LA
'Galaxy games on the road have our highest average attendance; with a few exceptions the LA Galaxy are our highest-rated team on television; LA Galaxy kit sales are among the highest and, without a doubt, there is more attention for David off the sports pages than any other MLS player.
'I travel outside of the United States on football-related business and people seem to ask about two things - when are the [New York] Cosmos coming into Major League Soccer and how is David Beckham doing?
'David, his personal manager, Simon Fuller, and Tim Leiweke of Galaxy owners AEG will go through a process after the Cup to try to determine what David's future is, but I certainly hope to have him back.'
If Galaxy cannot hold on to their big star, the next best option would be to recruit someone of Lampard's stature.
It is understood his name has been discussed.
However, given his engagement to TV presenter Christine Bleakley, moving his career 6,000 miles away could be problematic.
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Although the former Footballer of the Year would consider he has a few seasons of top-level football left in him, at 33 he could relish a new challenge.
At the end of his contract Beckham could even buy an MLS club for a knockdown price of $10million (about ?6.25m), terms secured when he joined the Galaxy in 2007.
Unlike the Premier League, you win your place in the MLS by setting up a franchise and paying a 'licence fee' to the league.
The going rate is about $50m (about ?31.25m).
His playing contract in LA ends after a post-season tour to Australia and the Far East.
But he is keen to play for Great Britain in next year's London Olympics, while Galaxy also want to offer him a new deal.
Beckham, 36, has expressed an interest in becoming a club owner. New York is favourite to form the next MLS team with the Cosmos.
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Source: Daily Mail
Source: Daily Mail