Moyes took on the biggest challenge of his career this week when he agreed to replace Sir Alex Ferguson as Manchester United manager at the end of the season.
The 50-year-old will, no doubt, be given a big transfer kitty to ensure that he starts his reign with a bang.
After scoring 30 goals for club and country this year, Bale is the hottest property in Europe right now, but Villas-Boas thinks even Manchester United couldn't afford to sign him this summer.
The Tottenham manager 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."
On Thursday, Bale picked up his Footballer of the Year award at the Football Writers' Association dinner in central London.
Less than two weeks earlier he had done the double at the PFA Awards, where he won Player of the Year and Young Player of the Year.
The more accolades he wins, the more rumours continue to circulate that Real Madrid will launch a big-money bid for the player this summer.
Bale showered praise on Tottenham and the Barclays Premier League as he collected his FWA prize, though, and Villas-Boas was more bullish than ever about his prospects of keeping the player this afternoon.
He said: "I have those guarantees (that Bale will stay).
"You can always make your own understanding from what the player says and how he feels.
"He is very, very driven to be successful but you can see that he is enjoying his football and all of the indications that I have are that he will continue."
Villas-Boas concedes the situation would be helped, though, if Bale signed an extension to his current contract, which runs out in three years' time.
"It would be good for him (to sign a new deal)," Villas-Boas said.
"I think he deserves it for the season he's had.
"Obviously we could put to bed every single speculation that's coming out, which we are calm about.
"It would be excellent and I think a reward for what he has achieved this season."
Spurs will look to Bale for inspiration on Sunday when they travel to Stoke knowing a win would move them into fourth ahead of Arsenal's game in hand against Wigan on Tuesday.
Villas-Boas said today that he was bracing himself for an "aggressive" match.
One person of interest to the Portuguese will be Stoke midfielder Charlie Adam, who has had a history of run-ins with Bale.
Adam caused crucial ankle ligament damage to the Welshman in 2011 while the Scot was on the books at Blackpool.
Then last summer, while Spurs were on pre-season tour in Baltimore, Adam, who was then at Liverpool, cynically fouled Tottenham's star man with a tackle that Villas-Boas said could have caused serious injury if he had caught him properly.
Villas-Boas conceded that Bale would not have been able to have such a fantastic season had Adam's challenge caused more damage, but he is confident that there will be no repeat on Sunday at the Britannia Stadium.
"I would be surprised if it happened again," Villas-Boas said.
"It is something that has happened between both players already but I am pretty sure nothing will happen.
"I don't think it will have an impact on Gareth. I just don't think, after the player acknowledged he made a bad tackle, it would happen again."
The good news for Villas-Boas is that midfielder Mousa Dembele, who missed the draw at Chelsea on Wednesday with a hamstring problem, is available for Sunday's game.
The Spurs boss added: "Dembele trains fully with the team on Saturday.
"We sent him to Holland, but now he is up for selection. He will come back fully fit."