The 25-year-old forward has endured a difficult campaign in the Spanish capital, with Los Blancos fans targeting the Wales international following the club’s Champions League exit.
Manchester United have been linked with a big-money move to sign the former Tottenham Hotspur forward, whilst Manchester City have also been touted as a possible suitor.
Former Liverpool defender Thompson reckons Bale could end up at Old Trafford, particularly in light of reports linking United shot stopper David De Gea with a transfer to Real Madrid.
Thompson told Sky Sports: “The timing of it would be right to get a fair amount of money plus because of the De Gea link it seems like that’s going to happen.
“I think it would work and he would relish the chance to come back to this country.”
Bale moved to Carlo Ancelotti’s side in a £85.3m deal from Tottenham Hotspur in 2013.
The former Southampton midfielder has scored 13 goals in 30 La Liga appearances for the 10-time European champions this season.
Los Blancos crashed out of the Champions League at the semi-final stage on Wednesday night after a 5-3 aggregate defeat by Juventus.
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