The 24-year-old was heavily linked with a move away from Brighton coming into the transfer window, with clubs including Arsenal said to be interested.
Those links eventually cooled down as the Seagulls are under no pressure to sell Bissouma after selling Ben White to Arsenal for £50m.
Liverpool, though, are claimed to have made an opening move for the Mali international this week.
The Reds have lost Georginio Wijnaldum on a free transfer this summer and have been linked with Bissouma for a while.
However, claims that they have stepped up their interest in the former Lille midfielder are wide of the mark.
With only five more days remaining in the transfer window and Brighton under no pressure to sell, Bissouma could be in line to stay at the Amex.
It remains to be seen if any of the midfielder’s potential suitors have plans to step up their interest in him before Tuesday’s transfer deadline.
