Los Colchoneros look set to stay without star forward Diego Costa at the end of the season and they see the Argentine as a good long-term replacement.
Il Corriere dello Sport has suggested that the La Liga side have established initial contact with the Nerazzurri as they hope to wrap up the deal for Icardi as soon as possible.
The 21-year-old only joined Inter from Sampdoria in the summer, but the Nerazzurri seem prepared to cash in on him in case of a good offer, especially after they learned Real Madrid youngster Alvaro Morata would be interested in a switch to Stadio Giuseppe Meazza.
Mauro Icardi has been in fine form this season, netting 8 times in 18 league outings, and scoring four goals in last two matches.
Inter Milan face a crunch tie with Parma next weekend and the Nerazzurri are 15/8 to claim maximum points.