The Sunday Express says United have noticed that talks are not going well between the Premier League strugglers and the England Under-21 international, who has only 18 months left on his contract.
Sessegnon, 18, helped Fulham to win promotion last season but appears reluctant to stay if they drop back into the Championship.
Ryan, and his twin brother Steven, have been Fulham players since 2008 - joining the youth set-up as eight-year-olds.
Despite his long stay in west London, Sessegnon has seen his playing time limited under new boss Claudio Ranieri, who suggested that the left-sided player needed to be 'more nasty' to secure a place in his first-team plans.
And United are ready to pay £50m for Sessegnon now that he is stalling on a new deal.