Spanish media sources say Real coach Jose Mourinho has identified Pazzini as their centre-forward solution and wants to bring him to Spain when the transfer market reopens.
Mourinho left a position on his squad vacant for a striker signing in January and had hopes of filling it with Santos star Neymar. But the Brazilian is unlikely to leave Santos until next summer, at the earliest, and Mourinho feels they remain an attacking option short.
Pazzini is admired by Mourinho and has struggled to get off the bench at crisis hit Inter so far this season.
Much will depend on new Inter coach Claudio Ranieri and his plans for the Italy international.