The Bosnian goalkeeper moved to the West London club in a £8million deal from Stoke City in the summer.
Begovic managed 20 appearances for the Blues while first-choice goalkeeper Thibaut Courtois was recovering from injury in the first half of the season.
However, since the return of the Belgian, Begovic has been reduced to a bench role at the club which he admits is not ideal.
"Certain things were put in place, conversations sounded good to me and I wanted to be part of a great club and help the team win trophies."
"It hasn't gone as planned, but hopefully that will change and the future will look a bit brighter."