The Sun says talks have stalled over the 18-year-old whizkidâ€™s new Liverpool contract.
The forward turned 18 last week and the Kop side expected talks to be a formality.
But Sterlingâ€™s progress has been so rapid he is now a wanted man.
He is a first-team regular at Anfield and made his England debut in the 4-2 friendly defeat against Sweden.
It would cause shockwaves if Sterling moved to Old Trafford.
He would become the first player to transfer between the two arch-enemies since Phil Chisnall nearly 50 years ago. But Anfield boss Brendan Rodgers has become anxious about Sterlingâ€™s future.