The Italian boss said earlier this week that he would be open to the exit of goalkeeper Given after favouring Joe Hart in the number one jersey for City's Premier League opener and Thursday's Europa League clash against FC Timisoara.
And he has now said, although he values the services of Robinho and Santa Cruz, he would not stand in their way if they request to leave.
Brazilian Robinho is attracting interest from Besiktas, Fenerbahce and Schalke, while Paraguay star Santa Cruz is being monitored by Fulham and West Ham, and neither player is likely to be content with a spot on the fringes of the City first team this term.
"If Robinho, Shay or Roque want to stay, I'm happy because they are fantastic players, but it is most important the players are happy," Mancini told The Times.
Mancini also added that the future of Robinho is likely to be decided within the next "five or six days".