The Spanish giants have long been linked with a move for Bale, who is enjoyed his best season to date with Spurs.
The Welshman has 28 goals in 47 appearances for club and country this term, and is reportedly a target for a host of leading European teams.
Real Madrid appear most keen, and could land their man if Spurs miss out on Champions League qualification this season.
Should they make the top four in the Premier League, Tottenham will be confident of keeping their leading man, and according to the Mirror there are further obstacles standing in the way of any deal.
Spurs are believed to have slapped a £100 million asking price on Bale in an attempt to ward of suitors - and the Mirror report that Madrid president Florentino Perez has allocated just £45 million to get the job done.
The paper claim that Madrid have made 'discreet enquiries' over the availability of Bale - and are willing to offer either Gonzalo Higuain or Angel di Maria as part of the deal.
But Tottenham are said to have knocked back any suggestions of letting Bale, who penned a new long-term deal until 2016 last summer, leave anytime soon.
Bale returned from an injury lay-off to inspire Spurs to a 3-1 victory over Manchester City on Sunday to help kick-start the north London club's final push for a top four spot.