The 25-year-old midfielder has been the centre of speculation for much of last season season.
His talent in controlling the game, and key role in the Seagulls’ record breaking season, has caught the eye of many.
Strong links with Aston Villa, who had a bid rejected in January, were the first of many.
Manchester United also have a reported interest in the midfielder as they look for a replacement for Paul Pogba, who is leaving the cub this summer.
Tottenham also seemed to be interested for a period.
However, the front-runner now appears to be Arsenal, following Bissouma’s hint on Instagram to a move there. The player seemingly signalling his wish for a move to the Gunners.
Bissouma shared on his Instagram two stories from an Arsenal fan who had posted: “I’ve been following up on Bissouma and I think he’s the one to replace Partey long term, he’s just 25” as well as.
"For me I think he and Tielemans should be our priority midfield, we must get @yves_bissouma at all costs @arsenal”.
As hints to a desired move go, that is not very subtle.
With the midfielder is just about to enter the last 12 months of his contract with Brighton and the price which the Seagulls can demand has lessened.
Following the rejected bid of £25 million from Aston Villa, it was reported in January that Brighton had placed a £50 million valuation on their star midfielder.
With his contract running down, they may have to accept less than that.
A bid in the region of £30 million, maybe less, may now be enough to see Brighton sell.
Not a bad price though for a player with just a year left on his contract. The demand and competition between clubs for Bissouma meaning Brighton could still get good money.
They also have the perfect man to step up for them next season if the Mali International should leave. 20-year-old Moises Caicedo.
The youngster – who Graham Potter described as ‘really fantatsic’ – has been impressive, putting in memorable performances in Brighton’s away win against Arsenal, and their thrashing of Manchester United at home.
He looks set to cement a place in the side next season, and push on to be Graham Potter’s new driving force in midfield.
Caicedo is similar in many ways to Bissouma. Able to dribble past opponents, a crisp passer of the ball, and constantly looking to play forwards.
His temperament at such a young age is also admirable. The Ecuador international has been able to control midfields against high calibre and experienced opposition, which should leave Seagulls fans in no doubt over whether he can fill Bissouma’s boots.
Caicedo partnered in midfield with Enock Mwepu, who has also impressed this season, would put Brighton in a position where they would retain all their midfield qualities, even with losing Bissouma.
With a ready-made replacement for Bissouma already in their ranks, Brighton fans could be forgiven for even getting excited about the prospect of an extra £25-30 million coming into the club, which can be used to bolster other areas.