Joint top-scorer in the Serie A along last season with Hellas Verona striker Luca Toni, Icardi has become one of the Nerazzurri's most important players since his switch from Sampdoria in 2013.
Following a breakout season at the San Siro, Icardi says he recently turned down the opportunity to join Real, in order to help Inter return to the Champions League.
"It’s true that Real Madrid wanted me," Icardi told Football Italia.
"But I asked to stay at Inter and my intention really was always to remain here. I knew that this year we would have a great squad.
"Now we are growing, so we hope to do well and get back into Europe. All this is tactical work that will take us closer to where Coach Mancini wants us to be."