Given, 37, has fallen out of favour at Villa under manager Paul Lambert and has made just nine appearances for the club since the end of the 2011-12 season.
The former Republic of Ireland international was linked with a switch to Liverpool in the recent transfer window that never materialised, while Championship outfit Doncaster Rovers also failed in a bid to sign the keeper.
With the Premier League's transfer window shut until January, meaning Given – who would prefer to remain in the top flight – will have to drop into the Football League if he moves out on loan.
The emergency loan window in the Football League opened on Monday and a loan switch could give the veteran a chance to play.
"As a footballer, as a player, that's all you want to do - play in front of big crowds, to show people you've still got the ability to play, hopefully in the Premier League," Given told TheBirmingham Mail.
"It's just frustrating that I'm not playing and it's hard to keep training and know there's no game at the end of the week.
"I'm fit as a fiddle, I feel really sharp and I'm just raring to get the chance if it comes along.
"Things can quickly change in football - injuries, suspensions, you never know - so if I do get my chance, then I've got to be ready to take it."
