Given has been ousted by England No. 1 Joe Hart at Eastlands, and said recently he was demoralised and would be happy to go anywhere he could get first-team action.
Newcastle are reportedly considering an appeal to the Premier League to allow Given to join on loan before the January transfer - citing the shoulder injury which has ruled out Steve Harper for three months.
Given spent 12 years at Newcastle before joining City for £8 million in 2009.
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Meanwhile, Sir Alex Ferguson has scotched rumours that Michael Owen could move to Aston Villa in January.
Owen would link up with former Liverpool boss Gerard Houllier at Villa Park, but Ferguson has no intention of letting Houllier steal him away from Old Trafford.
"He's (Houlllier) wasting his time there, " Ferguson said. "I understand Michael's frustration - he's exactly right - but it's because Berbatov started the season so well, then the international break came, It's difficult.
"We've go this Carling Cup game on Wednesday and he'll start that. He'll get enough football, Michael. It's just the early season with the internationals that disrupt you."