The Colombia international failed to nail down a regular starting role under Antonio Conte last season, and his fortunes did not improve with Cristian Stellini or Ryan Mason at the helm.
During a 3-2 loss to Bournemouth in April, Sanchez - who had come off the bench - was booed by the home crowd before being hastily withdrawn, in an episode which was expected to mark the end of his Spurs career.
The 27-year-old's deal now has fewer than 12 months left to run, although he was included in the matchday squad for last weekend's 2-2 draw with Brentford over Eric Dier.
Sanchez was brought on as a substitute at the Gtech Community Stadium following a head injury to Cristian Romero, whose possible absence this weekend could open the door for the Colombian to start against Manchester United on Saturday.
However, any minutes against the Red Devils may prove to be Sanchez's final appearance in a Spurs shirt, as The Telegraph reports that the ex-Ajax man has emerged as a transfer target for Monaco.
The Ligue 1 giants lost Axel Disasi to Chelsea earlier this summer and have signed Mohammed Salisu to replace him, but the former Southampton man is currently out injured.
As Sanchez will be free to leave Tottenham for nothing in 2024, the Lilywhites are expected to sanction a sale for the right price this summer and had accepted a £12.9m bid from Spartak Moscow.
Sanchez had reservations about a move to Russia, though, while interest from Galatasaray is yet to lead to anything, allowing Monaco to position themselves at the head of the queue.
Tottenham paid £35.9m to bring Sanchez to North London from Ajax in 2017, and the centre-back has come up with five goals and one assist in 206 matches for the Lilywhites in all tournaments.
However, the South American was restricted to a mere eight Premier League starts in the 2022-23 campaign and also played a mere 19 minutes across Spurs' eight Champions League fixtures.
Ange Postecoglou has already strengthened at the back with two summer signings, bringing in Micky van de Ven and Ashley Phillips from Wolfsburg and Blackburn Rovers respectively.
The Spurs boss is still thought to be open to more defensive additions, and a move for Bayer Leverkusen's Edmond Tapsoba has been mooted, but the Burkina Faso international is rated at £50m by the Bundesliga side.
The Lilywhites have also been put off by Crystal Palace's £60m valuation of Marc Guehi, while Fulham's Tosin Adarabioyo would coincidentally prefer to join Monaco this summer.
Tottenham have already let Joe Rodon leave on loan for Leeds United this summer, while Inter Milan are believed to be working on a deal to sign Japhet Tanganga.