Mali international Bissouma, who is set to enter the final year of his contract at the Amex Stadium, is expected to undergo a Spurs medical later this week.
The 25-year-old has been linked with a host of Albion's Premier League rivals due to his standout form on the south coast, including Steven Gerrard's Aston Villa.
Tottenham boss Antonio Conte is eager to boost his central midfield options, which currently include Pierre-Emile Hojbjerg, Rodrigo Bentancur and Oliver Skipp, while Harry Winks is likely to leave the club this summer.
Bissouma joined Brighton from French club Lille for a reported £15million in 2018.
He has scored six goals in 124 appearances in all competitions during his time in Sussex, including 26 top-flight outings last term as the Seagulls secured ninth spot - the highest finish in the club's history.
Bissouma could become Conte's third signing of the summer as he prepares for Champions League football next term.
The Italian coach has already recruited winger Ivan Perisic from Inter Milan and goalkeeper Fraser Forster from Southampton, both on free transfers.