Madrid already have their full quota of non-EU stars with James Rodriguez, Danilo and Casemiro currently filling those spots.
Real Madrid had reportedly been set to offer Bale a new deal that would see him commit his long-term future to the club.
However, that may now provide a headache for Zinedine Zidane's side following the UK electorate's decision to leave the EU, a process which is reportedly set to take two years.
Bale moved to Real Madrid in 2013 for a world-record fee and has gone on to win the Champions League twice during his time with Los Blancos.
