The 29-year-old is wanted by the Cherries this month and reports claim the Blues are already looking for a replacement.
Celtic goalkeeper Craig Gordon is one of those said to be on Chelsea's radar, while they are also keeping tabs on Galatasaray's Fernando Muslera.
However, Conte has stated he has no plans to sell Begovic and that he will start in the FA Cup against Brentford.
"Yes Begovic starts, but Begovic is a Chelsea player - it is important to understand this," said Conte.
"He is a Chelsea player and Begovic, for me, stays.