The 28-year-old was a consistent fixture of the Blaugrana XI in the first half of the 2021-22 season, but injuries and transfers saw him lose his place in the team under Xavi.
Pierre-Emerick Aubameyang and Ferran Torres quickly moved ahead of Depay in the pecking order, and he only started five La Liga matches since January.
The former Lyon man also penned a two-year deal upon his arrival at Camp Nou in 2021, meaning that he could depart as a free agent at the end of next season.
With Robert Lewandowski and Raphinha now confirmed to be joining La Blaugrana, as well as Ousmane Dembele penning a new deal, Depay is surplus to requirements at Camp Nou.
A return to the Premier League has been mooted for Depay, who endured an underwhelming spell at Manchester United between 2015 and 2017 before signing for Lyon.
According to Spanish outlet Sport, Tottenham have touched base with Depay's entourage and are willing to table a bid of €17m (£14.5m) to sign the Netherlands international.
However, Barcelona are said to be holding out for an offer of €20m (£17m) for Depay, who has accepted that he will not be a regular starter under Xavi next season.
Depay only scored two goals in 33 Premier League games for Man United, though, and he is said to be reluctant to return to the English top flight.
Interested clubs in Italy are supposedly being put off by Barca's price tag, and Depay has no intention of being used in a player-plus-cash deal with Sevilla for Jules Kounde.
Depay ended his debut season at Barcelona with 13 goals and two assists from 37 games in all tournaments, with eight of those strikes coming in his first 14 La Liga matches for the club.
Tottenham have already negotiated with Barcelona for the loan signing of Clement Lenglet, while also boosting their attacking options with the £60m capture of Richarlison from Everton.
Djed Spence has also been pictured in a Tottenham kit ahead of his move from Middlesbrough, and Antonio Conte has refused to shut the door on further signings this summer.
"We are always looking to improve the squad if there is the possibility," Conte told reporters in South Korea when questioned on Spence's imminent arrival.
Yves Bissouma, Ivan Perisic and Fraser Forster have also arrived at the Tottenham Hotspur Stadium during a busy summer of spending for the North London club.