The Spurs midfielder has been sidelined with the problem for four games but his manager is hopeful he can return to action in the coming weeks
Dembele picked up the problem whilst on international duty with Belgium, and has missed Spurs' last four games.
However, Villas-Boas is confident the injury is not too serious and that he can have his summer signing back in action sooner rather than later.
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"We want to avoid surgery if we can," Villas-Boas told reporters.
"If there happens to be surgery I think we are looking for one month, one month and a half.
"Hopefully that will not happen because we have some good indications the player will be back in one week or two weeks."