Both the Gazzetta dello Sport and the Corriere dello Sport are suggesting that the 27-year-old is wanted by the Beneamata.
Inter are apparently hoping to net the player initially on a one-year loan and then buy him outright in the summer of 2014.
Modric was a major transfer investment for Real last summer when they paid around €35m to Tottenham for him.
A number of Real players could be set for summer moves given the likelihood that boss Jose Mourinho will quit the outfit.
Modric, three goals in 47 Real appearances this term, is a Croatian international central midfielder.
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- Sports & Recreation
- Corriere dello Sport
- Gazzetta dello Sport