A report from the Sunday Times claims that the Reds boss sees the Albion man as a potential replacement for Gini Wijnaldum, who is expected to leave Anfield in the coming months.
It is understood that the German has been impressed by the 24-year-old performances on the south coast this season, and is now looking to determine whether or not he would be a good fit for his dressing room on Merseyside.
Liverpool are not the only side keen on Bissouma, however, with Manchester City and Arsenal also said to be keeping tabs on the Malian, while Olympique Marseille are weighing up a move that would take him back to French football.
The midfielder signed for Brighton from Lille back in 2018.
The Times also suggest that Bissouma himself would be open to a summer transfer, and has requested a potential exit at the end of the season.
Albion are said to be open to a possible transfer, but would demand around £40 million for the player before considering a sale.
So far this season, the box-to-box talent has featured 33 times in the Premier League for the Seagulls, and has drawn praise from the likes of Liverpool legend John Barnes, who believes he has what it takes to be a success at Anfield.
“He is strong defensively, he works hard, he plays the ball quickly and every now and then when he needs to dribble, as much as we don’t speak about Brighton, you know he can do it, because he has [in the past].
“Of all the players playing in England, that could fit the template of Liverpool’s midfield three, he is one of them.
“He [plays] like Georginio Wijnaldum, although he doesn’t attack as much as ‘Gini’ [Wijnaldum], because Brighton play a different style of football, when Bissouma wants to he can. He is 24 and young, he would be a great fit.”