The former Republic of Ireland international has found himself frozen out of things at Villa Park under Paul Lambert.
Brag Guzan replaced him as No.1 keeper last season and Given has been pushed down to third-choice keeper by the arrival of Jed Steer in the summer.
The 37-year-old admits he has found it very frustrating to not be playing and that he will consider his options when the transfer window reopens in the New Year.
"When you've played virtually every game throughout your career it's difficult - especially when you think you should still be playing," Given told The Sun on Sunday.
"I'm disappointed I'm not involved and I'll just train hard until January and hope something comes up."