Dembele quickly become a fans' favourite at White Hart Lane following his deadline day move from Fulham, but Tottenham have had to do without the playmaker for the last four games after he aggravated a hip injury while on international duty with Belgium.
The 25-year-old struggled with the problem while at Fulham, and initial scans on the area failed to detect whether he had seriously aggravated the injury while playing against Scotland.
The worst case scenario for Villas-Boas is that he will be without the player for six weeks, but the Tottenham boss is confident that will not be the case.
"We want to avoid surgery if we can," Villas-Boas said.
"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.
"It's a pain that goes away or happened to go away when he was at Fulham for two or three days and the pain went away but it is still there.
"He can't move himself properly so he will have a deeper scan on the injury so we can assess it properly."
Although Tottenham have moved up to fourth in the Barclays Premier League despite Dembele's absence, Villas-Boas could do with the former AZ Alkmaar man back soon as he faces up to a tough run of matches following Saturday's home game against Wigan.
Spurs failed to follow up their win over Southampton with another victory last night when they were knocked out of the Capital One Cup by Norwich.
One of the main talking points from the 2-1 defeat was the team's late penalty, which came about after Kyle Walker went down under the challenge of Marc Tierney.
Tierney said he did not touch Walker and Canaries boss Chris Hughton said the England right-back "made a meal" of the challenge.
Having grown up on a council estate in Sheffield, Walker took umbrage at Hughton's suggestion he went down too easily.
"I'm from up north. I'm not going to go down softly," Walker told Press Association Sport at an event to publicise the Topps Match Attax Tour.
"I thought I got a clip so I went down. It was a foul.
"The referee has awarded a penalty, or the linesman did. They were close enough to see it.
"If I felt I was touched then I am going to go down. That's it."
Walker was keen to focus on this weekend's game, which he thinks will be crucial to Tottenham's efforts to achieve the Champions League place that evaded them last term.
"It's massively important that we bounce back from that game and get back to winning ways," Walker said.
"No disrespect to Wigan, but out of the (next) three (games) this is the easiest game.
"We want to get a good run into Wigan and then hopefully that will give us momentum to get to City and then hopefully after the international break we can go to Arsenal and get the three points there."
Emmanuel Adebayor could be available for Saturday's game after making a steady recovery from injury and illness.
The Togo striker is reported to have become frustrated at his lack of game time this season, but Villas-Boas says the player must be patient given the excellent form of Jermain Defoe this term.
He said: "Whenever he came on he did well. He wants to be part of the team, but Defoe is doing well. He has eight goals in five games and that is the goalscoring ability you want for your team.
"Ade(bayor) is there too but has to be more patient at the moment, but I'm sure after these setbacks he can make a good run in the team too."
:: Kyle Walker was in Enfield meeting fans and children on the Topps Match Attax Tour, following the launch of the Match Attax Championship Edition football trading card game. For further information, please visit toppsfootball.co.uk
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