Real Madrid have been chasing the Argentina international for a number of months but their interest has peaked recently because of misfiring forward Karim Benzema.
The Frenchman has only scored two La Liga goals this term as Los Blancos sit fourth in the table.
Boss Zinedine Zidane is adamant that the club will not make any more signings this window but president Florentino Perez may have one more trick up his sleeve.
Icardi made a post on his Instagram account late last night of a photo of a path with a slogan written in Italian over the top.
And when converted to English it read: “Being able to say goodbye is to grow.”
He captured it with “Bye bye” and an emoji of a waving hand, indicating that he could be leaving Inter.
The 24-year-old also disabled comments on the posts so supporters of both Inter and Real remain stumped as to the message.
Icardi has scored 18 goals so far this season and is tipped for a bright future.
He started his career with Sampdoria before moving to the San Siro in 2013.
The striker has since racked up over 150 appearances scoring 93 goals.