A number of clubs are tracking Rotherham midfielder Lee Frecklington, Sky Sports understands.
Barcelona and Brazil defender Dani Alves expects his future to be resolved in a meeting with the Nou Camp club.
Given has recently enjoyed a successful loan spell with Sky Bet Championship club Middlesbrough where he kept 10 clean sheets in 16 matches.
Unfortunately for Given, the deal could not be extended through to the end of the season as Villa would have been unable to recall him at 24 hours' notice.
The Republic of Ireland international, who is out of favour at Villa but still has another two years remaining on his contract, can join another club on loan.
That is Given's hope ahead of a permanent move at the end of the season.
"Hopefully something will happen in the summer somewhere," he told the Birmingham Mail.
"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 is 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."