Although the North Londoners are far from keen to lose their star man, they are aware that it may be impossible to turn down a big money move.
If he does move on Griezmann is believed to be one of their top targets, with the 21-year-old having made a big impact in the Spanish top tier.
Reports suggest that manager Andre Villas-Boas sees him as an ideal replacement for Bale, and somebody who could adapt to his set-up easily.
Bale has suggested that he would be open to a move away from the club in the future, and could push forward any plans should Spurs miss out on Champions League football for next season.
Real Madrid are thought to be favourites for his signature, due to the working relationship between the two clubs.
But, Manchester United are also in the hunt as they look to replace a number of aging first-team stars.