The news is a blow to the French champions, who have had a poor start to the season.
Ait-Fana scored a crucial goal for Montpellier in their last Champions League game, where they picked up their first ever point in the competition against Schalke.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?