Tottenham will have to pay up to £63m to land Lyon's Tanguy Ndombele this summer.
Sky Sports News understands negotiations between the two clubs are continuing, although no deal is close to being agreed.
The versatile midfielder, who cost Lyon just £7m last summer, is presently on holiday and will take that time to consider his future before making a decision on his return in July.
Pochettino is desperate to bolster his midfield options alongside Harry Winks.
Over the weekend, Ndombele hailed Tottenham as a "big club" and admitted he is interested in signing for Mauricio Pochettino.
Speaking to French publication Telefoot, he said: "It's true that Tottenham are a great team - a big club. They finished fourth in their league, they were finalists in the Champions League.
"They are a big club like many others. Which player would not be interested in a big club?"
Ndombele has been capped four times by the French national team and is on the radar of several top European clubs including Manchester United, Paris Saint-Germain and Juventus.