Sky Sports is reporting that the Belgian defender is open to extending his stay at the north London club beyond the summer.
As things stand, Vertonghen will be free to speak to foreign clubs in January as his current contract is due to expire at the end of the season.
The same story says that the likes of AS Roma and Bayer Leverkusen have been keeping an eye on Vertonghen’s situation at White Hart Lane.
It is claimed in the same article that former discussions between Daniel Levy and Vertonghen’s representatives are yet to take place.
The 32-year-old defender was an unused substitute during the 4-2 win over Olympiakos in the Champions League on Tuesday night.
Mourinho has been settling into life in charge at Tottenham after being brought in as Mauricio Pochettino’s successor at the north London club last week.
Spurs will return to Premier League action this weekend when they host Bournemouth in the top flight on Saturday afternoon.
They will then prepare for their trip to Old Trafford to take on Mourinho’s former club Manchester United next week.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news