The 28-year-old threw his career at the Bernabeu up in the air straight after firing them to a third successive Champions League title on Saturday.
The forward said he would sit down and discuss his issues with Barnett – the owner and chairman of Stellar Group – in the close season, but it now appears things are moving at an increased pace.
It has now been decided to press ahead with a meeting between Barnett and Real officials.
Manchester United and Chelsea are reportedly interested in Bale, but Sky Sports News understands he is not a target for Spurs despite a contract clause that allows them to compete with any successful bid from a Premier League club.
He is still contracted until 2022 and on wages considerably higher than any of Spurs’ current squad. That coupled with an inevitably sizeable transfer fee would make any deal financially unfeasible for his former club.
Bale became a world star at White Hart Lane before a then world-record £86m move to Real Madrid, where he was won four Champions Leagues, a La Liga title, a Copa del Rey, and two Spanish Super Cups in five years.
But reports in England and Spain claim Bale’s relationship with manager Zinedine Zidane has broken down during a campaign in which he has made 20 league starts and six extras as a substitute.
After scoring twice in Real’s 3-1 win over Liverpool in Kiev – the first a stunning overhead kick – Bale said: “I feel that I need to be playing every week.
“It’s something that I’ve always wanted to do and it hasn’t happened here this season for one reason or another.
“I really don’t know [where I will be]. I’m going to have to sit down and discuss it with my agent. Maybe I’ll be staying here, maybe not. We’ll sit down in the summer and hopefully resolve this issue.”