Villas-Boas tells Bale to stick with Spurs
Although the newly-crowned footballer of the year is currently under contract until 2016, Spurs are keen to give Bale a pay rise to fend off interest from Real after netting 20 Premier League goals already this season.
Bale will be looking to add to that impressive haul when Spurs visit Stoke on Sunday in a match crucial to the north Londoners' hopes of qualifying for the Champions League, which would be a major boost to their hopes of persuading the Welsh midfielder to remain at White Hart Lane.
"It would be good for him to sign a new contract," said Villas-Boas, whose fifth-placed side are one point behind fourth placed Arsenal and three behind third placed Chelsea.
"I think he deserves it for the season he's had. Obviously we could put to bed every single speculation that's coming out.
"It would be excellent and I think a reward for what he has achieved this season."
Villas-Boas has yet to beat Stoke in two attempts - drawing 0-0 in both games - and he knows the hostile Britannia Stadium will present a tricky test of Spurs' European ambitions again this weekend.
"We have to do our job in the two remaining fixtures and it's time for somebody to slip up," he added.
"At the moment, we can only focus on ourselves, try to get the maximum points possible and wait for something to happen.
"The Premier League can change in a weekend. Everything is still a possibility."
Tottenham's Togo striker Emmanuel Adebayor, who scored in their 2-2 draw at Chelsea on Wednesday, has called on his team-mates to go for broke in their last two matches.
"We have two games left and they will be like two cup finals for us," he said.
"We play against Stoke then Sunderland at home and we have every chance to do it. We have to believe we can do it and then we can do it.
"We have to keep going, keep fighting and those games are critical now, we have to win those matches."
Stoke manager Tony Pulis has vowed to play his part in keeping the race for Champions League places as competitive as possible.
Pulis has steered his side to safety after reaching 41 points with a draw at Sunderland last Monday, yet he says Villas-Boas should not expect any favours from Stoke.
The club will be staging a day of celebrations to mark their 150th anniversary and they want to round off the day in perfect fashion.
"We're relaxed in a way we hope we can now put in a good performance against Spurs," he said.
"It's a big game for us, and it celebrates the 150th anniversary of the club. What we have to do is concentrate on giving Tottenham a decent game."
Pulis admits he has had a tough time from supporters this season, but he believes he has answered them by keeping the club up again.
"It's so important that this club stayed in the Premier League. Some people want more - that's up to them. They're entitled to their opinions."
Pulis says the temptation to rest key players is tempered by the fact that Spurs have plenty to play for.
"I think it's all about how we play rather than Spurs," he said. "I hope we can have a go at Tottenham and get the crowd behind us.
"We have a responsibility to the Premier League to put out as strong a team as we can. That's what we'll do."