Begovic made the move to Stamford Bridge from Stoke City for just £8m last season but is now been linked with a switch over to Everton.
The Bosnian made 21 appearances last season replacing Thibaut Courtois who was out with a knee injury.
The 29-year-old is set to sit the season out on the bench as the Blues Belgium star is fully match fit and will be remaining in west London.
Begovic has three years left on his current deal at Chelsea.
It’s been said the west Londoners will want at least £8m to part with The Bosnian.