The former Ajax man has been expected to bid farewell to the Premier League after his own fans turned on him during Spurs' defeat against Bournemouth last season.
Sanchez had come off the bench to replace the injured Clement Lenglet but was soon substituted himself by Cristian Stellini, being booed by the home crowd in the process as Tottenham suffered a 3-2 loss.
The 27-year-old was already below Eric Dier, Cristian Romero and Ben Davies in the defensive pecking order, while new arrival Micky van de Ven has established himself as Romero's first-choice partner in Ange Postecoglou's four-man backline.
As a result, the door was open for Sanchez to leave the club earlier in the summer window, and Spartak Moscow apparently had a £12.9m bid accepted, but the defender was reluctant to move to Russia.
Galatasaray and Monaco have also been mooted as potential destinations for the out-of-favour Sanchez, but according to The Athletic, Rennes recently approached Spurs with an official bid.
The French side supposedly offered €9m (£7.7m) to buy the Colombia international out of the final year of his deal before he leaves on a free transfer, but the report states that Tottenham turned down the offer.
Despite Sanchez's contract situation, Spurs are understood to be after at least €15m (£12.9m) and as much as €20m (£17.2m) to let the 27-year-old leave, having forked out €42m (£36.1m) to sign him from Ajax in 2017.
Furthermore, Tottenham would only have a few days to bring in a replacement should Sanchez depart, and the South American remains a part of Postecoglou's plans, having replaced the injured Romero during their opening Premier League draw with Brentford on August 13.
Sanchez has since been an unused substitute against Manchester United and Bournemouth, but he will be expected to come into the starting XI for Tuesday's EFL Cup second-round tie with Fulham, and Spurs are no longer actively trying to sell him after he proved his worth as a backup option.
Sanchez has come up with five goals and one assist in 206 matches for Spurs over the past six seasons, but while the Colombian might remain in North London, Spurs are looking to move some other defenders on.
As is the case with Sanchez, England international Dier only has one year left to run on his contract and is on the chopping block, having not made a single Premier League squad so far this season.
The 29-year-old could supposedly be used as a makeweight in talks with Fulham for Tosin Adarabioyo, while Scottish champions Celtic are also keeping a close eye on developments.
However, Dier is still determined to fight for his place in the squad under Postecoglou, but if he is not loaned out or sold this summer, he will depart when his contract runs out at the end of the 2023-24 season.
Tottenham's only defensive outgoing so far this summer has been Joe Rodon, who has joined Leeds United on loan, but Japhet Tanganga, Djed Spence and Sergio Reguilon are all expected to clear out their lockers ahead of Friday's deadline, as are midfield duo Tanguy Ndombele and Manchester United-linked Pierre-Emile Hojbjerg.