The Scot is due to take over at Old Trafford on July 1, when his current deal with Everton runs out and he is expected to utilise the cash made available to mould the Premier League champions.
The Spurs boss knows that his star man has attracted attention all across Europe with the likes of Real Madrid and Barcelona monitoring his progress.
The Portuguese is eager for the Welsh winger to sign a new deal with the north London club, but his decision may depend on whether they can secure Champions League football next season.
Villas-Boas said: "I'm pretty sure that whatever David does in the market will be excellent. But to get a player of Gareth's dimension is firstly not in our interests but also very, very difficult to get."