Antonio Conte is determined to land his No.1 target from Napoli this summer and the Blues are ready to up their offer in a bid to prise him away from Italy.
Chelsea have already seen an opening bid of £42m bid rejected for the Senegalese defender.
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"We've decided to leave for economic reasons… Chelsea still want him and there's time to close a deal."
Koulibaly's arrival could spell concerns for Gary Cahill's first team future.
Conte could adopt his favoured back-three formation that could see his position alongside John Terry threatened.