City have been keen on luring the 21-year-old to Eastlands and now the English and German league seasons are over, the transfer could be concluded this week.
"We are quite close to signing him," Mancini told the Manchester Evening News. "Boateng is a good player, a young player and strong.
"He plays for the Germany national team and there is a good chance to get him.
"He can play three different positions; central defence, right full-back or in midfield. If we find a player like that it is better for us."
Mancini has vowed to bring in some fresh faces this summer, although the Italian has admitted his job will be made more difficult by the failure to secure a Champions League berth.