The Spurs coach stated while the new Loftus Road chief may be interested in bringing former players to his struggling squad in January, the English duo are definitely not for sale
Parker has yet to play for Spurs this season since suffering an Achilles injury in pre-season, while Dawson has struggled for game time because of the form of youngster Steven Caulker early on in the campaign.
However, despite Redknapp's interest in bringing his former players into the fold for the struggling Rangers, the Portuguese coach has sought to cut off any potential loan or permanent moves for the pair.
"It's hard for me to say what QPR's decision-making will be in the transfer window," he told reporters. "Obviously Harry knows these players very well and if he has to add to his squad he will certainly look to our players, but we don't want to sell these two or loan them."
Spurs could move into fourth place with a win against Swansea on Sunday afternoon, but Villas-Boas admits the side has missed the drive of captain Parker in the centre of the pitch - and would be loathe to let the midfielder go.
He continued: "Everybody has to compete [for places] but we recognise the importance of the player and rate him very, very highly. He offers us even more possibilities in midfield. Experience, leadership, communication skills, all that.
"We have good recoverers of the ball in Sandro and Mousa [Dembele] in that midfield area but Scotty takes us to another level."
While Dawson has been available yet used rarely by Villas-Boas, the coach feels letting the centre-back leave would weaken a crucial area of his team, particularly with Younes Kaboul still recovering from a long-term injury.
"Younes went through this period of injury and there is that period where you have to recover and come back into the game," he added. "It takes two or three weeks to gain match fitness. Also we have used Jan [Vertonghen] at left-back so it is not excessive in terms of numbers."
Parker is in line to take a place on the bench for the Sunday afternoon clash against Swansea, and his return would surely boost Spurs' challenge for a Champions League place.
QPR meanwhile recorded their first win of the season on Saturday by beating Fulham 2-1 at Loftus Road, and moved off the bottom of the Premier League in the process, but are still five points from safety.