Lampard saw Galaxy in action this week as the rumour mill went into a frenzy over an imminent deal.
It has been reported that Chelsea may be tempted to allow him to leave on a free transfer as he is one of their top earners on £160,000 a week and will also be owed a loyalty bonus of £1.75million should he see out his contract.
However, the 34-year-old, who missed playing in Euro 2012 due to a thigh injury, will report back for pre-season training at Chelsea and manager Roberto di Matteo believes he will stay at Stamford Bridge.
He said: “I’m expecting him [Lampard] to return healthy and fit. I spoke to him, he is feeling very good and looking forward to next season.”
It is more likely Lampard would join Galaxy next summer, especially as there has been no indication that he will get the contract extension he desires from Chelsea, says the London Evening Standard.