The Blues are keen to snap up the young midfielder but Sir Alex Ferguson is keen to keep a hold of him, according to The Mirror.
Questions surrounding Pogba’s future have arisen from the fact that his contract runs out at the end of the season, which means the Red Devils could lose him return for a small compensation fee.
The report has suggested Andre Villas-Boas’ club have been watching the midfielder’s reserve performances and have already sounded out the 18-year-old’s representatives.
It also claims that some in Pogba’s team are looking to secure a payment of around £3 million from the club who manage to sign him.
AC Milan have also been credited with an interest in signing a player who was the subject of a furore over his move to United from French club Le Havre in 2009.
Pogba is also a France Under-19 international and made his Premier League debut in the victory against Stoke City earlier this season.