The 22-year-old left-sider is on a season-long loan at the Stadium of Light from Spurs, and he has made a big impression on Wearside.
Sunderland boss Martin O'Neill had already revealed his desire to sign Rose on a permanent basis, but that option has now been ruled out.
"Completely impossible," said Villas-Boas when asked if he would allow Rose to leave on a permanent deal.
"We have big expectations for him in the future. Our idea is that he comes back to Tottenham next year.
"We appreciate what he's been doing over here and it's been a great experience.
"He's been extremely well managed. We can't give away a player of his quality."
Sunderland have, though, been boosted by the news that Rose will not be recalled in January.
"Danny is a great talent, it's encouraging that it seems he will stay with us until the end of the season," said O'Neill.
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