The 34-year-old Stamford Bridge midfielder is set to leave the Blues at the end of the season, as his contract expires in the summer, and it seems unlikely he will renew.
A number of clubs have been linked with a move for the England international, and the report now claims Manchester United and Arsenal have jumped to the front of the queue to sign Lampard.
According to the report, Chelsea chief executive Ron Gourlay has informed Lampard that his contract will not be extended, and the club now expects the midfielder to leave the club on a free at the end of the current campaign.
Talks were reportedly held between Lampard and Chelsea before the Blues' match against QPR last Wednesday, but instead of offering the former-West Ham star a new deal, the club told Lampard he is free to leave in six months time.
The 34-year-old remains a fans' favourite at Stamford Bridge, and his 12-year stint at the club has coincided with a period of sustained success, including three Premier League titles, four FA Cups and one Champions League.
And Lampard demonstrated his value to Chelsea this season, scoring the match-winning goals against Everton last weekend, before coming off the bench to score Chelsea's fifth in their 5-1 victory over Southampton in the FA Cup third round on Saturday.
The Daily Mail reports that Sir Alex Ferguson has already told Lampard that he would love to bring him to Old Trafford, but the report claims Ferguson accepts it's unlikely to happen.
Arsenal are also reportedly tracking developments, but Lampard is believed to be unwilling to move to another London club after more than a decade at Chelsea.
LA Galaxy also remain an option for the Blues legend, but the American club's season starts in March, and David Beckham's former team are thought to want Lampard signed before their campaign gets underway.