1138 GMT August 19, 2019
The 24-year-old striker has been linked with a multimillion-euro move to the reigning Spanish and European champion, AFP reported.
The Argentine has attracted Real's interest after scoring 18 times in the league.
His wife Wanda Nara, who is also his agent, is an avid user of social media.
And the forward quoted the Argentine song 'Adios' with the phrase "to say goodbye is to grow" on his official Instagram page, along with the caption "bye bye", and a waving emoji.
Inter insisted no negotiation were underway with Real Madrid or other clubs. Moreover, the €110-million termination clause cannot be exercised in January.
Coach Luciano Spalletti has insisted Icardi is committed to Inter but the coming months could be decisive for the Argentine's stay in Milan.
After Inter's storming start to the season Spalletti's side has faltered and has not won since December 3.
Inter sits fourth in Serie A table but the final Champions League spot for next season is under threat.
Forty-eight hours from the end of the transfer window, the words of Inter’s captain inflamed a day of negotiations with Paris Saint-Germain to bring Argentine midfielder Javier Pastore to Milan.