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Jose Mourinho is also in the race to sign the Real Madrid star
Mourinho's side are yet to secure Champions League football next season with their best chance of returning to Europe's elite competition by winning the Europa League.
But with Chelsea on course for the Premier League title and Conte working his magic in west London, Bale could be open to a move to the Blues if they come knocking.
Bale has scored nine goals in all competitions for Madrid this season and is under contract until 2022.