Hazard, 27, has long been linked with a move to the Spanish giants and there is bound to be plenty of fresh speculation linking him with a switch to the Bernabeu after Chelsea FC missed out on qualification for the Champions League.
The Belgian playmaker has constantly insisted that he is happy at Stamford Bridge but it remains to be seen if Real Madrid will indeed make a move for him this summer.
And former Liverpool FC midfielder Redknapp feels that Chelsea FC could use the move to their advantage and try to sign Wales star Bale as part of the deal.
Bale has been linked with a switch away from Real Madrid recently after he struggled for both form and fitness this season.
And Redknapp feels that both Manchester United and Chelsea FC would be wise to consider moves for Bale this summer.
Writing in his column for the Daily Mail, Redknapp said: “[Manchester] United won’t be the only ones after him [Bale].
“If Eden Hazard goes to Real Madrid, I’m sure Chelsea would be keen on a swap deal.
“After a season of limited gametime, Bale will be keen to prove he is still a world-class talent. What better way to do so than inspire a team to properly challenge City?”
Chelsea FC will aim to end the season on a positive note by beating Manchester United in the FA Cup final at Wembley on Saturday evening.
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