Conte capped off a disappointing season with a piece of silverware on Saturday as Chelsea saw off Manchester United 1-0 in the FA Cup final at Wembley.
However, after over a year of tension with the board over transfers and problems behind the scenes, it appears his reign is coming to the end, with the aformentioned source claiming that the 'Blues' will pay up the £9m he would be owed for the final year of his contract.
Enrique is believed to be Chelsea's number one target to replace the Italian, though Monaco's Leandardo Jardim and Napoli's Maurizio Sarri.
Conte was left frustrated last summer as Chelsea failed to bring in a number of his top transfer targets, including Romelu Lukaku, Virgil Van Dijk and Alex Sandro and he admitted on Saturday that victory in the FA Cup was unlikely to change anything regarding his future.
“I don’t think winning the FA Cup changes anything about my future. A win or a loss cannot change that," he explained.