For the Welshman's part, he is thought to be keen on the switch, but as it stands, Spurs are holding firm.
It got Sports Mole thinking: What else could that money get you? Below is a team in a 4-3-3 formation made up of players who have switched clubs this summer, coming to a total of £2m less than what Bale would cost Los Blancos.
Maarten Stekelenburg (Roma to Fulham, £3m)
It was a move that had been expected to take place in January, but in the closing stages Roma pulled the plug. The Dutch international finally completed his transfer to Craven Cottage earlier in the summer, though. The 30-year-old will provide the Cottagers with a wealth of experience, having played in the final of a World Cup.
Daniel Carvajal (Bayer Leverkusen to Real Madrid, £4m)
Los Blancos were so reluctant to let the right-back go last year that they included a buy-back clause in the deal that took him to Germany. Having shone in the Bundesliga with Leverkusen, the Spanish outfit took little time in exercising their right to re-sign the 21-year-old.
Raul Albiol (Real Madrid to Napoli, £10m)
He may have struggled for regular starting action under Jose Mourinho, but Albiol is still regarded to be an extremely competent defender. He was linked with a host of clubs, but eventually opted for Napoli, who are managed by his fellow Spaniard Rafael Benitez. Still only 27, the centre-back could well have his best years ahead of him.
Jan Kirchhoff (Mainz to Bayern Munich, free)
The German champions have spent big money so far and as a result Kirchhoff's arrival at the Allianz Arena has gone somewhat under the radar. The 22-year-old arrived on a free transfer from Mainz, but is regarded to be one of the most promising talents in German football. Some believe that he has a chance of playing at next year's World Cup.
Fernando Amorebieta (Athletic Bilbao to Fulham, free)
Fulham manager Martin Jol has made an effort to bring down the average age of his squad this summer. At 28, Amorebieta is now in his prime years. The Venezuela international will add some tenacity to the Fulham rearguard, having earned himself a reputation in Spain as a tough-tackling defender down the years.
Kevin Strootman (PSV Eindhoven to Roma, £14m)
It appeared for a long while that the Dutch international was going to be the man to fill the void in the Manchester United midfield. The move never materialised, though, and Roma swooped to take him to Italy. While not the most creative of players, Strootman is more comfortable stopping opposition attacks.
Paulinho (Corinthians to Tottenham Hotspur, £17m)
All-round midfielder players are a rare commodity these days, but Spurs have landed one. Paulinho is an old fashioned box-to-box footballer who is effective in both halves of the pitch. The 25-year-old impressed as part of the Brazil side that won the recent Confederations Cup.
Isco (Malaga to Real Madrid, £28m)
Even at the age of 21, big things will be expected of Isco this season. He has arrived at the Bernabeu having played a leading role in the Spain team that emerged victorious from the Under-21 European Championships in Israel. The attacking midfielder showed during a recent friendly against LA Galaxy that he is already comfortable in his new surroundings.
Fernando Llorente (Athletic Bilbao to Juventus, free)
With a proven goalscoring record, there won't have been many better players available on a free transfer than Llorente in recent years. The 28-year-old will add some height to the Juventus forward line, as well as the ability to hold up possession.
Mario Gomez (Bayern Munich to Fiorentina, £17m)
If nothing else, Gomez guarantees his team goals. Even though he was second choice at Bayern last season, he still found the net on 19 occasions. In the two campaigns before that, he hit a remarkable 80 goals. Those figures make the 28-year-old's move to Fiorentina, rather than to one of Europe's biggest clubs, all the stranger.
Carlos Tevez (Manchester City to Juventus, £10m)
Regardless of his antics off the pitch during his time in England, the Argentine still showed what a good footballer he was. Being mobile and a hard worker, the 29-year-old could potentially go on to form an extremely profitable partnership with Llorente.