Given is set to make his first appearance of the season in Wednesday's Carling Cup tie at West Brom, just three days after Mancini confirmed he could leave City in January.
The Republic of Ireland star has lost out to Joe Hart in the battle to be City's number one keeper this season and, although he remained at Eastlands during the last days of the transfer window, is likely to seek pastures new when it re-opens again in the New Year.
Already Newcastle boss Chris Hughton has been forced to play down speculation that he might try and get Given back to St James' Park on an emergency loan following the injury sustained by Steve Harper.
Now Mancini has stepped in to confirm that Given is still wanted by City and will not be released without the buying club coming up with substantial funds.
"Shay is an important player and he will cost someone a lot of money," said the City boss.
"I said Shay could leave the club if he wants and we have a good option but if he stayed it would be OK for me."
Mancini has also repeated his assurance that he has not had a bust-up with £25million striker Emmanuel Adebayor, who could also come into contention for tomorrow's trip to the Hawthorns.
"It is false that I fought in the dressing room or the pitch with Emmanuel Adebayor," said Mancini.
"We discussed his situation, that is all."
After reaching the semi-finals of last season's competition before losing out in a thrilling two-legged encounter with Manchester United, Mancini is keen to make amends and end the Blues' 34-year trophy drought.
However, his hopes of beating West Brom tomorrow have been hampered by an injury list that shows no signs of reducing as Jerome Boateng and Joleon Lescott remain sidelined, combined with the knowledge that City require fresh bodies for Saturday lunchtime's encounter with champions Chelsea.
"We have a lot of problems at the moment with certain players injured," he said.
"Also, we must change maybe seven players. If not it will be impossible for them to play against Chelsea because it is a lunchtime game on Saturday and they don't have time to recover."