Sissoko, 22, is out of contract with the Ligue 1 club next summer. He had initially seemed destined for a move to Marseille or Monaco, but has reportedly made clear that he intends to join the likes of Hatem Ben Arfa, Yohan Cabaye and Mathieu Debuchy at St James's Park.
Negotiations between Sissoko's representatives and Newcastle officials are scheduled for Wednesday, though L'Equipe also says the player's agent is in London for talks with Queens Park Rangers.
While his destination remains unclear, it is certain that Sissoko, who played in Toulouse's 2-1 win over Nancy on Saturday night, is on his way out of the club he joined in 2003.
"Moussa Sissoko has three choices: extend his contract with Toulouse, leave this winter or stay on the bench until June," club president Olivier Sadran told BeIN Sport.
"If he extends his contract, he'll have the chance to leave at the end of the season with a very big bonus. There are offers from Marseille and Monaco, and some English clubs are trying to get involved. If he doesn't decide quickly, I'll take a decision."