Spurs have been monitoring Gallagher since last summer. They also considered the 23-year-old in the recently closed January transfer window.
Manager Ange Postecoglou is reportedly a massive admirer of the Epsom-born star and would love to work with him.
Chelsea have been struggling to agree a new contract with Gallagher who has 18 months left on his deal.
They have tried to pawn him off for pure profit to balance the books following their £1 billion transfer outlay in the past four transfer windows.
The Blues have handed long-term contracts to Reece James and Levi Colwill, but Gallagher’s extension has been hanging in the balance.
The box-to-box midfielder has garnered interest from some of the top clubs in the Premier League, including Liverpool, Spurs, Newcastle United and West Ham United.
The Cobham Academy graduate is the beating heart of Chelsea’s midfield and has recently rediscovered his shooting boots after blanking for the first half of the season.
Gallagher bagged a double as Chelsea beat Crystal Palace 3-1 yesterday and also opened the scoring in their 3-1 win over Aston Villa in the FA Cup.
He would be a fantastic coup for Tottenham and they will be desperate to place themselves ahead of the queue for his signature.
Chelsea manager Mauricio Pochettino wants Gallagher to stay, and the player does not want to leave Stamford Bridge.
The club have made several terrible transfer decisions over the past two years, but letting Gallagher join a rival would be top of their list of atrocious calls.
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