The 22-year-old has impressed since being sent on a season-long loan at the Stadium of Light, where he has been a consitent performer at left-back.
He was unable to play against his parent club in Saturday's 2-1 Spurs win and was clearly missed by the Sunderland back four.
Black Cats boss Martin O'Neill had already revealed his desire to sign Rose on a permanent basis, but that option has now been ruled out by Villas-Boas.
"[It's] completely impossible," said Villas-Boas.
"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."
O'Neill did reveal that Rose won't be recalled in January and is set to remain on Wearside until the end of the season.