Tottenham ended the 2016/17 campaign seven points behind Chelsea and were the only side to run Antonio Conte's team close for first place.
Atletico Madrid star Griezmann has been heavily linked with an exit from the La Liga club, with Manchester United keen on his signature.
However, United's interest in the Frenchman has cooled in recent days and Griezmann has taken to Twitter to express his happiness about staying in Spain.
He has a release clause of £86million and Wilkins believes Spurs should attempt to bring him to north London to strengthen their attacking credentials.
What Antoine Griezmann has said about his future Tue, May 30, 2017
What has Manchester United target Antoine Griezmann said about his future?
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Speaking at a press conference with the France national team in May
Ray Wilkins believes Antoine Griezmann would be a great signing for Tottenham
Add Antoine Griezmann alongside Harry Kane with Dele sitting in behind him, you've got three players who score goals
Ray Wilkins on potential of Tottenham signing Antoine Griezmann
"They need to spend in a forward position because if Harry Kane gets injured, they're going to struggle," the former Chelsea and Manchester United midfielder said on Sky Sports.
"Wouldn't Tottenham look wonderful with (Hugo) Lloris, that back three of (Eric) Dier, (Jan) Vertonghen, (Toby) Alderweireld, (Danny) Rose on the left, (Kyle) Walker on the right, (Victor) Wanyama and (Mousa) Dembele, Dele, Griezmann, Harry Kane?
"You've got a chance of winning, you've already got the best defence, now you add Griezmann alongside Harry Kane with Dele sitting in behind him, you've got three players who score goals.
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Antoine Griezmann has been linked with Manchester United but they have cooled their interest
"Defensively you're sound, I don't hear any noise from Tottenham that they're going in for somebody but a Griezmann signing would be something very special.
"I know it goes beyond their pay structure and Mr (Daniel) Levy would have a lot of people rapping on his door asking for rises.
"But if Tottenham think they are going to win the league with the guys they got at the moment, then I think they're barking up the wrong tree for next season."
Griezmann scored 26 goals in all competitions for Atletico last season.