Conte was finally dismissed last week following a whole summer of speculation.
Maurizio Sarri is the new Chelsea manager having reportedly been lined up for weeks.
Conte will receive his £9million salary that he is entitled to for the final year of his contract.
However The Times report that the Italian now feels he deserves to be compensated for loss of future earnings and the damage to his career.
It’s claimed that Conte was resigned to leaving Chelsea since January after a collapse in relationship with the board.
Conte reportedly heard nothing from the Blues for several weeks at the end of last season before being summoned back for pre-season training.
He took charge of the players for four days before a meeting with chairman Bruce Buck brought an end to his tenure.
It’s believed Conte’s legal team will argue that Chelsea’s delay in sacking him cost their client a year of his career.
That’s because all top management jobs in Europe have been filled with jobs at Real Madrid and PSG both having been available this summer.
Real Madrid reportedly sounded out Conte for the role after Zinedine Zidane left before handing the position to Julen Lopetegui.
The Italy managerial role was also recently vacant though Conte did not apply for them and he is set to claim he was committed to Chelsea.