Transfer Latest: Lampard agrees terms with LA Galaxy
The midfielder has been told by the three-time Premier League champions that he will not be offered an extension on his current 150,000-pounds-a-week deal when it expires at the end of the season, bringing to an end a 12-year association with the Stamford Bridge club.
Manchester United and Arsenal are both monitoring Lampard's situation, while Everton have already had a three-year offer rejected - but the MLS side appear to have won the race, according to reports.
"It's all but done," a source in the United States told the football website.
An LA Galaxy spokesman would not confirm or deny the news, only telling reporters that head coach Bruce Arena publicly acknowledged interest in Lampard on Thursday.
"I wouldn't be surprised if over the next week or so, we're going to have some kind of decision we're going to make with a Designated Player," Arena told reporters.
"We wouldn't rule (a move for Lampard) out. It's always a possibility."
Lampard, Chelsea' second-highest all-time goalscorer, was free to sign a pre-contract with a foreign club from the start of January, and is open to a move to the United States for personal as well as professional reasons.
During Chelsea's tour in North America last summer, Lampard expressed an interest in playing in MLS but admitted that he would wait to see if Chelsea would extend his contract first.
"I am not sure (about a future in MLS)," Lampard said at the time.
"I have another year on my contract at Chelsea and we have a big season ahead of us with the Super Cup and the Club World Cup in December. It's up to Chelsea to speak with me about my future and, at that time, I'll speak with them.
"I wouldn't rule anything out at the moment."