The Mali international midfielder has been excellent for Albion this season and is widely tipped to leave the Amex Stadium during the summer.
Bissouma's agent Michael N'Cho increased speculation earlier this campaign by stating there is "considerable interest" in his client with Manchester United, Liverpool, Arsenal, Monaco and Real Madrid all poised.
Brighton have five games remaining this season and continue their battle to maintain their Premier League status, and Bissouma, who is contracted until June 2023, will be expected to play a key role in that scrap.
Brighton signed the Ivory Coast born midfielder from Lille for £15m in 2018 and if they do sell, the club will hope to more than double their money on the 24-year-old.
Arsenal remain in the running to land him as he could team up with former Lille players Gabriel Magalhaes and Nicolas Pepe.
Gunners boss Mikel Arteta is also said to be a huge admirer and believes Bissouma could form a successful midfield partnership with Thomas Partey.
Arsenal paid Atletico Madrid £45m last October to land Ghanaian international Party and Brighton will hope to fetch a similar fee – perhaps slightly higher as Bissouma is a few years younger. Some believe up to £50m.
Liverpool however are favourites and will look to bolster their midfield, especially if Georginio Wijnaldum departs this summer.
Albion fans will be disappointed to lose their key man but in many ways he represents a perfect signing for the club.
Brighton's preferred strategy is to recruit and develop the finest young talents, such as Tariq Lamptey and Alexis Mac Allisiter, and give them the opportunity to perform in the top flight.
If all goes to plan, Brighton get one, two or three good seasons and then sell for a healthy profit. Southampton have been doing this for years.
The key to this is of course is succession planning and in Jakub Moder, 21, and recent arrival Moises Caicedo, 19, Brighton appear to have done just that.
Poland international Moder was signed for £10m last summer and recalled from his loan at Lech Poznan earlier this season. The athletic 6ft 3in box to box midfielder has featured on the left of midfield in recent matches but Graham Potter insists his future will be in a more central position.
Caicedo, after lengthy and complex transfer negotiations with Independiente del Valle and numerous agents, signed last January and has impressed the management. He has featured in the matchday squads but is yet to make his Premier League debut.
The Ecuador international was wanted by Manchester United, West Ham and AC Milan and is one of South America's most promising midfielders. The £4.5m signing could well be ready for regular first team action next season.
Bissouma's displays have highlighted his class and value to this Brighton team but Potter remains relaxed about his future.
"The exciting thing for Yves is he can improve some more," said Potter last week.
"He’s not at the top. But he’s got incredible potential and incredible talent. Like any player, we have to be honest and sensible enough to know that if [they are] good enough to play at that level and [have] that opportunity, then we shouldn’t be scared of that.
"At the same time, Yves is happy. He knows he’s in an environment here [where] people care for him, look after him and want the best for him. He’s not perfect; he’s not the finished article; he’s still got things to improve. That’s really exciting for me as a coach."
In the short-term Bissouma still has a vital role to play on the south coast, especially with Leeds visiting the Amex this Saturday.
But, should he depart this summer, it will represent a good deal for all parties and give the next ones of Moder, Caicedo and academy graduate Steven Alzate, their chance to do the same.