The Spurs manager insists the Black Cats will not be able to sign the England Under-21 left-back on a permanent deal, after some impressive displays on Wearside so far this term
The 22-year-old has impressed during his loan spell at the Stadium of Light, putting in a string of excellent performances, earning praise from Martin O'Neill and adulation from Black Cats supporters.
However, the Portuguese has also taken note of the youngster's progress on Wearside and is unwilling to let him join Sunderland on a full transfer when his loan spell comes to an end in May.
He told reporters: "A permanent move is impossible because we have great expectations for the player, he has a bright future. 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."
This news came as a bitter blow to O'Neill, whose Sunderland side were beaten 2-1 by Tottenham on Saturday, as he had hoped to secure a deal for Rose during the January transfer window.
The 60-year-old admitted Villas-Boas' statement was frustrating but feels a lot can change in football and mooted a high bid might sway Spurs' decision.
He said: "I'm really disappointed he said that. Lots of things can happen though, if we put in an offer of £38 million I think he would taxi him up here himself. At this moment he's doing very well and in many aspects it's helping Tottenham out.
"There weren't too many takers of Danny when we came in for him and he's enjoyed it immensely here. There wasn't a rush for him at that stage but he's done remarkably well for us. If he does stay now that's encouraging.
"He thinks he has really good talent and that Danny will stay until the end of the season. That's encouraging for us and we'll see what develops after that."
O'Neill praised the spirit of his side after the defeat to Spurs, but admitted that his players had simply been outclassed.
He added: "We played with a lot of commitment and a lot of heart. We got ourselves in front just before half-time but it was disappointing to concede two goals in two minutes that knocked us back.
"Tottenham had chances to make it three but we kept going until the end and I couldn't fault the commitment of the team at all.
"We had to fight pretty hard all afternoon. They are a very fine side Tottenham."