According to Dutch newspaper De Telegraaf, Ajax are actively working to secure the 30-year-old's signature, though competition for the free agent is believed to be significant among clubs across the continent.
The Dutch outlet reports that several clubs from Europe's top five leagues have also shown interest in Bissouma, leaving him with strong options as he considers the next chapter of his career following his exit from north London.
The defensive midfielder left Tottenham at the end of June following four seasons at the club, in which he made 111 appearances since arriving from Brighton in a deal worth around £30 million.
Bissouma joined Spurs from Brighton in the summer of 2022, having previously impressed during four seasons on the south coast, and has been a free agent since leaving Tottenham this summer without a new club to call home.
The midfielder struggled for regular football during his time in north London, particularly under the club's most recent head coaches, and was ultimately allowed to leave when his contract expired at the end of the season without a fee being received.
Ajax have been credited with interest in Bissouma for much of the summer, though a move has yet to be finalised as the Amsterdam club weigh up their options in midfield alongside their other targets in the position.
Reports elsewhere have also linked Bissouma with clubs in Serie A and Turkey, though the midfielder is said to be keen on remaining in a major European league if the right opportunity arises before the winter transfer window opens in January.
Ajax technical director Jordi Cruyff is understood to be personally keen on the deal, having already overseen a number of significant additions to the Amsterdam club's squad during the summer window.