Ferguson is a long-time admirer of the player and tried to get him before he even joined Chelsea.
According to the Sun, it is unlikely a deal will be done this month, when a fee would be involved, while Lampard is also keen to see out the rest of the season at Stamford Bridge.
Lampard has been told he is no longer wanted at Stamford Bridge, with his contract set to run out soon.
According to the report, United are prepared to offer him a one-year deal in the summer, with the promise of a second year if everything goes well.
Contact has already been made from Old Trafford to Lampard's representatives, the report said. (ANI )