Vertonghen’s future at the club is up in the air, after the defender hinted he may look to leave in the summer should the club fail to qualify for the Champions League.
The Belgian is reportedly a target for Barcelona, who are in the market for a replacement for club legend Carlos Puyol, who is retiring at the end of the season.
Chelsea’s David Luiz, Arsenal’s Thomas Vermaelen, and Liverpool’s Daniel Agger have also been mentioned as possible targets.
Tottenham are already on the lookout for a replacement should Vertonghen depart, and Valencia’s Mathieu is understood to be a top target.
The 30-year-old Frenchman is a centre back who can also play at left back, and Tottenham have watched him in action several times this season.
He is under contract with the La Liga club until 2017, with a reported buy-out-clause of £17million, although Spurs chairman Daniel Levy remains confident a deal can be completed for less.
Monaco are also understood to be interested in the defender, who has been on the fringes of the France national team, although the Ligue 1 club are understood to have other primary targets.