The 24-year-old has been identified as a potential replacement for Georginio Wijnaldum at Anfield, according to ESPN.
The Dutchman appears likely to leave next summer when his contract expires, and Liverpool are considering a January bid for Bissouma to take his place in the squad.
The Seagulls are likely to demand around £30 million for the Mali international's services but United, Monaco and two unnamed Spanish clubs are also tracking the midfielder.
Bissouma joined Brighton for £15m from Lille in 2018 and has made 12 Premier League appearances for Graham Potter’s side this season, scoring one goal.
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