Spurs boss Antonio Conte is keen to bolster his midfield as they prepare for Champions League football next season.
Bissouma has attracted interest from a number of Premier League clubs, including Aston Villa, Arsenal and Newcastle, but Tottenham have jumped to the head of list and the Mali international is set for a medical later this week.
Carragher said: "Clubs will not just be looking at Bissouma this summer, they will be bidding for him.
Carragher was talking after Bissouma delivered an awesome display against Everton last season.
"The biggest bright spark from the game was the performance of Bissouma, who was the Man of the Match.
But not just the best player on the pitch, the best player by a mile on the pitch, he really was," the former England defender told Sky Sports .
"You looked at him and he really does look like a top-quality player.
"He was excellent at Old Trafford [against Manchester United ] for Brighton and he just looked head and shoulders above everyone on the pitch [versus Everton].”
His fine displays last season also brought praise Match of the Day presenter Gary Lineker. The former England striker posted on Twitter: "What an exceptional footballer Yves Bissouma is."