The City boss is under pressure after failing to defend the Premier League title, and the report claims Atletico Madrid manager Diego Simeone is the fourth and latest name added to the wishlist.
PSG boss Carlo Ancelotti, Malaga's Manuel Pellegrini and Borussia Dortmund's Jurgen Klopp are the three other managers under consideration by the Etihad Stadium hierarchy.
Ancelotti remains one of the favourites, and is expected to leave the Parc des Princes at the end of the season. He has a clause in his contract that allows him to quit - but he must trigger it before April 30.
City's recently appointed chief executive Ferran Soriano has made contact with Ancelotti's agent regarding a summer appointment, but the former-Chelsea manager is also wanted by Real Madrid.
Manuel Pellegrini has also impressed the City executives - the Chilean helped Malaga to the Champions League quarter-finals and within a few seconds of the semi-final this season.
The problem for City could be the fact that Klopp, Pellegrini and Ancelotti will all probably be in demand this summer, with Chelsea, Real Madrid and PSG are likely to be in the market for a new boss.
For that reason City have added Simeone to their shortlist. The Atletico Madrid manager has won the Europa League and UEFA Super Cup for the club since taking charge in December 2011.
Mancini's failure in the league this term, coupled with City's poor Champions League showing, means his position is vulnerable, despite guiding the club to another FA Cup final.