Newcastle manager Joe Kinnear revealed on Friday that the Tyneside club had given City permission to speak to Given, after weeks of speculation over his future.
It is understood personal terms have already been agreed and the the deal is now close to going through ahead of Monday evening's transfer deadline.
Newcastle tacitly accepted the Irishman's impending departure last week when they secured deputy Steve Harper on a new three-year contract.
However, the news that he is having a medical will have come as a blow to those fans who hoped he might not leave St James' before the deadline.
Given has spent more than 11 years on Tyneside since his arrival from Blackburn, and his loyalty has never been in question.
However, comments released by his solicitor Michael Kennedy as the transfer window opened indicated he had lost patience with the ongoing turmoil on and off the pitch and signalled his intention to secure a move away.
City's interest has been clear in recent weeks, as they embark upon a massive spending spree, and it remains to be seen whether Kinnear can invest the proceeds - if indeed, he gets the cash - in an attempt to drag the club out of relegation trouble.
Midfielder Kevin Nolan arrived in a £4 million move from Bolton on Friday, but the club's need is huge with Michael Owen and Joey Barton having joined the long-term casualty list once again, ironically, after Wednesday night's 2-1 defeat at City.
Charles N'Zogbia, too, could be on his way, as Newcastle and Wigan thrash out a player-plus-cash deal, with Ryan Taylor moving in the opposite direction.