Goalkeeper Given arrived at Villa Park from Manchester City in 2011, but subsequently lost his spot as the club's number one to American Brad Guzan.
The 37-year-old spent 16 games on loan at Championship outfit Middlesbrough this season, keeping 10 clean sheets, but Villa opted against sanctioning a longer deal because doing so would have made them unable to recall the Irishman on an emergency basis if the need arose.
However, Given harbours hopes of leaving on loan again between now and the end of the season, and will be looking for a permanent transfer come the end of the campaign.
"It looks like I will be going back and I won't be playing much football," he told the Birmingham Mail.
"That's the situation I am in. Hopefully something will happen in the summer somewhere.
"It has been really frustrating not playing. That's obvious for everyone to see and the window doesn't open until the summer, so maybe there's a Championship club out there who might want me.
"I might go back out on loan again somewhere before the end of March.
"Aston Villa want me out of the door, so something might happen."
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