Icardi has been mooted as a potential target for Los Blancos by sources in both Spain and Italy amid doubts over the Madrid futures of Gareth Bale, Karim Benzema and club talisman Cristiano Ronaldo.
The Argentine striker has been in sensational form this season for the Serie A pacesetters with 16 goals in 15 appearances.
It has been claimed Real are ready to trigger Icardi’s release clause, which is believed to be 110million euros, but Nerazzurri sporting director Piero Ausilio says the Spanish giants are yet to make any contact.
“There’s no need to convince him into staying at Inter, he has a long contract here and his will is very clear,” Ausilio told reporters.
“He’s our captain and he wants to win with this shirt. All this goes beyond contracts and clauses.
“Madrid haven’t called us, but it would be their job to convince Mauro into abandoning a project like ours, in which he’s the leading light.
“Furthermore, the clause isn’t a problem. Icardi or [Juventus forward Gonzalo] Higuain? I’ll stick with Mauro.”
Southampton have announced plans for a two-week tour of China as part of their pre-season preparations for the 2018-19 season.