Icardi is one of the leading marksmen in in Europe this season with 18 goals in 20 matches for Inter.
And his displays have led to speculation he could be on his way out of the San Siro.
Both Chelsea and Manchester United have been rumoured to be interested in the Argentina international in the past.
But Real have been leading the way for his signature with further questions marks over Karim Benzema’s future.
That’s because it is said Real have already conducted a medical assessment in private.
Icardi’s release clause currently stands out close to £98million but Inter sporting director Piero Ausillo recently claimed the Serie A giants are confident they could extend the forward’s contract.
Mauro Icardi is one of the leading goalscorers in all of Europe this season
Karim Benzema faces an uncertain future at Real Madrid
“I won’t rule out that, without any appointments set right now because he has a very long contract, we could in future sit down and talk about something different.”