Mark Hughes has already suggested he would love the opportunity of seeing Given wearing the City goalkeeper shirt.
And after Saturday's FA Cup debacle against Nottingham Forest, City are ready to make additions to their squad.
Toon Braced For City Offer For Given!
If the deal goes through, Given could link up with former Newcastle players Craig Bellamy and Scott Parker, who have been heavily linked with the Eastlands outfit.
Hughes: "I am sure we will be making more offers this week.
"It is about getting the balance and the pitch of the offer right. If you do that, more often than not a deal can be concluded quickly.
"Long drawn-out deals tend to test everyone's patience so it is better to look at the market, look at what you think the club that has the player would want and go in at that level."