The Bosnia and Herzegovina international currently sits second to Thibaut Courtois. Begovic has been heavily linked with a transfer to Bournemouth the past few days.
The Daily Mirror claim that the Cherries has submitted a £10m bid for the former Stoke City man. however, the Blues want £12m.
Conte, however, did not confirm whether or not the offer had come from Eddie Howe’s side, only that a bid had been received and that he and the Stamford Bridge hierarchy were considering it. He did not reveal how much had been offered.