The 20-year-old left winger - whose current deal runs until 2017 - was one of the highlights for the Netherlands at the World Cup and has been attracting interest from Manchester United, but Spurs are set to make the first move.
United boss Louis van Gaal, who brought the best out of Depay as he led Netherlands to third place in Brazil before stepping down to take over at Old Trafford, has advised the youngster to remain at PSV for another season.
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The former Bayern Munich coach has privately told Depay that his career would be best served by remaining in the Eredivisie for another season before seeking a transfer abroad, potentially to United.
However, Depay appears to be ready to move on in the current window and claimed on Saturday that he would consider his future should offers arrive from Europe's top leagues.
He told De Telegraaf: "I'm having a good time at PSV but, if big clubs from big leagues come to me, I will think about it. There is more than enough interest but it is also an option to stay at PSV.
"I understand that the fans want me to play in Eindhoven next season. I see a lot of children with my name on their shirt. I'm proud of that but I'm the one who decides how my career looks and no one else."
Van Gaal will likely now have to act fast if he wants to seal a deal to take Depay to Old Trafford, with Spurs ready to signal their intent with a big opening offer.
PSV, for its part, is willing to sell one of its prized assets, although the Premier League duo could face competition from some of Europe's other elite clubs, with Real Madrid also keeping tabs on Depay's situation.
New Spurs boss Mauricio Pochettino has already brought in Eric Dier, Ben Davies and Michel Vorm this summer and is closing in on a deal for centre-back Mateo Musacchio, while Jay Rodriguez and Morgan Schneiderlin could also make the switch to White Hart Lane.