The Welshman, who enjoyed six years in north London, joined Real in a world-record £86 million deal in 2013 but has endured a turbulent spell at Real, and has come in for intense criticism during his second season with the European champions.
Bale's performance against Juventus in the Champions League earlier this week attracted further negative attention - with Roy Keane labelling the Welshman anonymous - but Pochettino says Spurs would welcome the 25-year-old back to England.
"If he is not comfortable in Madrid, we keep his place warm back here," he told reporters. "We are open for him!"
Pochettino, however, believes that Bale will eventually adapt to life at the Bernabeu, and has urged Real fans to show patience with the forward.
"It is, of course, not easy when you arrive at a huge club like Real Madrid, and the way they play. Gareth Bale has the quality to make a success, he just needs time," he added.
"When [Zinedine] Zidane went to Real Madrid, the first season was very difficult for him, with a lot of critics. He needed time to adapt.
"The cultures are very different between England and Spain. It is very difficult for English players to arrive in Spain, there is a Siesta, you eat later.
"It is better when you come from Spain to England, when you go there, you need one or two seasons to adapt.
"I think here it is better to develop your passion in your job as a player or manager, but in Spain, for the weather, for the culture, it is difficult to adapt when you come from England. He just needs time."
Goal understands that Bale intends to reject a potential move to Manchester United this summer in favour of remaining at Real.