The 24-year-old Malian has had an impressive season with the Seagulls, making 36 Premier League appearances and emerging a one of the club’s best players.
There are rumours that he could move on in the near future, and he is believed to be valued at around £40m.
Bissouma took to social media to post a picture of himself sitting on a sofa in Dubai.
And along with the photo he left the caption: “mom told me watch out they will love you a lot less when you go up my son, you will see time break some friendships”, along with an emoji of a writing hand.
Some have taken this to be a reference to Bissouma’s future, and believe he is hinting at the need to move on from Brighton.
It comes as Seagulls owner Tony Bloom admitted that he would be open to letting some of the side’s top players if the price is right.
He told The Athletic: “The more big clubs there are interested in our players, the more we’re doing right, so I’m delighted with that.
“We know some of our best players are not going to be with us forever. If the right offer comes along – and it has to be the right offer – and they want to go, then they will leave.
“I foresee the vast majority [of the squad] to be here at the beginning of next season.”
Bissouma’s time at French side Lille may prove vital to Arsenal’s hopes of persuading him to move to the Emirates.
He is said to keep in touch with his former Lille teammates Nicolas Pepe and Gabriel Magalhaes, both of whom joined the Gunners within the last two years.
Brighton manager Graham Potter, meanwhile, was unable to guarantee Bissouma would stay at the Amex earlier this week.
When asked if he knew anything, Potter said: “Not really. He’s contracted with us
“As far as I know he’s going to report to pre-season like everyone else.
“But it’s football. Like anything, in the summer we have to make some good decisions and improve the football club.”