The Wales international has been frozen out by Real manager Zinedine Zidane and said earlier this month that he was open to returning to the Premier League.
It has been reported that Spurs and Manchester United are interested in signing Bale but Jose Mourinho appears to be leading the race to land the 31-year-old.
"It's close but not done," Bale's agent Jonathan Barnett told AFP. "It's a complicated deal."
Bale has two years left on a contract that pays him a reported salary of about £600,000 ($775,000) a week at Real.
It has been reported the Spanish club would be willing to pay some of that salary to finally move on from their troubled relationship with the forward.
Bale left Tottenham for Real in 2013 for a then world-record fee of £85 million.
He has won four Champions League titles and two La Liga crowns during his time in Spain, but his turbulent relationship with Zidane has left him a peripheral player.
He started just one match when the 2019/20 season resumed after the coronavirus hiatus as Real clinched their first la Liga title since 2017.
Bale almost joined Chinese Super League club Jiangsu Suning last year before Real pulled the plug on the deal and he has accused the club of making it "very difficult" to leave.
The winger still has an emotional attachment to Tottenham after joining the club from Southampton as a teenager and developing into one of the world's most exciting forwards.
Former Spurs boss Harry Redknapp, who managed Bale for four years at Tottenham, said he would bring "that little bit of magic" to Mourinho's side, who lost their first game of the Premier League season to Everton.
"It would be a fantastic signing for the club," he told BBC Radio Wales. "It would be great for Gareth to get back playing again. He's such a talent, such a great player. It's a waste to see him not playing."
As well as their interest in Bale, Tottenham are reported to be in talks with Real about left-back Sergio Reguilon, who had also been linked to United.