United are struggling to cope with the sheer volume of injuries that have hit their squad this season, and have slumped to back to back Premier League defeats against Blackburn and Newcastle.
The Red Devils are particularly struggling in midfield with injuries, with Tom Cleverly, Anderson and Michael Carrick all enduring spells on the sidelines this season, while Darren Fletcher remains some way off returning to action as he continues to recover from a serious bowel condition.
Now the paper reports boss Sir Alex Ferguson is eyeing up bringing the 33-year-old to Old Trafford to ease his injury worries, with the player himself said to be open to the idea of switching allegiances.
Lampard has found first team opportunities hard to come by this season as boss Andre Villas-Boas attempts to remodel the Blues aging squad.
The England International, who has made 504 appearances for Chelsea since joining the club in 2001, has admitted to being frustrated at being consigned to the substitutes bench, although he did score the winner in the Blues' 2-1 victory against Wolves last weekend.
The former West Ham man’s wages could be an issue, with Chelsea said to be paying him over £140,000 a week while the United owners would have to be persuaded to take a punt on a player with no sell-on value.
The Mail suggests Lampard would be open to listening to other offers after falling down the pecking order in Villas-Boas thoughts behind younger players such as Raul Meireles and Oriol Romeu.
Lampard has 18 months left on his current deal with Chelsea and has previously expressed a desire to sign a new contract at Stamford Bridge and finish his career in west London.