The ambitious Blues are expected to be busy in the transfer market again this summer, with the club's owners prepared to bankroll a number of big-money acquisitions.
Among those mentioned as possible arrivals at Eastlands is Aston Villa winger Milner, with City having already seen a £20million approach knocked back.
It remains to be seen whether City will test Villa's resolve with a second bid, as money is no issue to Roberto Mancini's men.
Blues goalkeeper Given believes the club would be advised to do all they can to secure his signature, with the Irishman mightily impressed by the England international during their time together at Newcastle United.
"He has had a great season at Aston Villa," Given told Sky Sports News.
"He played some fantastic football when I was at Newcastle with him as well. He's a quality all round player. He has got bags of ability, a great left foot and right foot, so he's a very good talent.
"If he comes to the club great, if he doesn't he has had a great time under Martin O'Neill at Aston Villa."
Whether City snatch Milner or not, Given is confident there will be big-name arrivals at Eastlands this summer.
The club are determined to force their way into the Champions League sooner rather than later and know they must be prepared to splash out in order to bring in players of that lofty standard.
"I do think we have got a good squad of players now," added Given.
"If players want to join the club they will look around the players we have already got here and see that it is a club really going places, and they will like to join that and help move the club forward again.
"I think next season we will be stronger and better. I am sure the manager is working hard to bring in some players over the summer.
"We are a club moving forward, that's for sure. We have got some great players in the squad and everything is set up for success.
"Rome wasn't built in a day but we are building the blocks to be a successful football club and that's where we want to go.
"We finished fifth last season, the highest finish ever for the club in the Premier League, so next season we want to step up to the next level."