The Italian wants to further strengthen his squad in this summer's transfer market and has highlighted the trio as his preferred signings.
Tottenham Hotspur playmaker Modric has been persistently linked with a move away from White Hart Lane since he requested a switch to Chelsea last summer.
It is believed that Mancini would have to pay around £35m for the Croatian's services, which is around the same fee that would be needed to prise Eden Hazard from Lille.
The Belgian winger is an alleged target of several Premier League clubs with City apparently leading the hunt for his signature.
Uruguayan striker Cavani, who has scored 27 goals in 46 games for Napoli this season, completes Mancini's transfer wishlist and would also cost £30m plus.