The teenager played a massive role in the Cottagers' promotion to the top-flight last season and so far, he has featured in 23 occasions in the Premier League.
According to The Express, the Red Devils are planning to test the Cottagers' resolve for the youngster during the summer, given the South London side appear likely to make an instant return to the Championship.
It is added that the Mancunian giants are monitoring Sessegnon's
contract which expires in 17 months' time and they could be willing to pay as much as £50m to lure him to Old Trafford.
Sessegnon has not overly impressed since the Cottagers' return to the Premier League with just two goals and five assists from the 16 starts and seven substitute appearances.
Still, United seem to be banking on the potential of the Cottagers' graduate, who has already shown his immense versatility of featuring at left-back, left midfield or on the left of a three-man attack front.