The ambitious Eastlands outfit just missed out on a Champions League place this season, although Mancini and co will not settle for just a top four place.
City only lost seven league games during the campaign - the same number as second-placed Manchester United - but too many draws cost them a higher finish.
The club have spent millions in the transfer market in recent years and while City have a squad that is the envy of many a Premier League manager, Given feels they still need to add one or two big names.
When asked whether he likes City to add more names to their squad this summer, Given told Sky Sports News: "I hope so.
"I want the club to keep moving forward and the more players we can get to helps to strengths the squad.
"We've got a very strong squad at the minute, don't get me wrong.
"If we can get a couple more world class players into the team it will really strengthen us for the campaign next year."
Given finished the campaign on the sidelines after dislocating his shoulder against Arsenal, an injury that saw him stretchered off the field in agony.
The Republic of Ireland ace is on the road to recovery and is excited about how well his rehabilitation is progressing.
"I'm working with the physiotherapist everyday and doing my rehab as you obviously need to do after an operation," he continued.
"I'm really positive that everything is going good so I'm really chuffed about it."
Meanwhile, Given has offered his support to England keeper Rob Green following his World Cup howler against USA on Saturday.
The West Ham shot-stopper gifted Clint Dempsey USA's equaliser in their Group C opener, a mistake that cost England two points as they were held 1-1.
Given has backed Green to bounce back from the disappointment as he believes he has proved in recent campaigns that he is a top class keeper.
"He's proved over the last number of seasons how good a keeper he is.
"I wished him well a couple of days ago. I dropped him a text and stuff.
"I hope he plays to be honest and does really well. It's one of the best football experiences of your life."