A dip in form of forwards Cristiano Ronaldo and Karim Benzema this season has led to speculation Madrid will seek to spend heavily on attacking reinforcements before 2018-19.
Bayern Munich's Robert Lewandowski continues to be linked with a move but Inter captain Icardi is also reported to be a prime target.
But Brazil great Ronaldo believes Icardi is happy at San Siro and is not sure if he would agree to a move.
"I'm convinced Icardi is happy at Inter, just as I was, even if I suffered from a lot of injuries and my departure didn't go as I had hoped," Ronaldo told Sky Sport Italia.
"But even though we don't know much about the transfer market, I think a lot of clubs are lining up for Icardi.
"Going to Madrid is every player's dream, but I don't know if it's his."
Ronaldo, who won the UEFA Cup during a five-year spell with Inter before joining Madrid in 2002, believes the Nerazzurri should stick with head coach Luciano Spalletti for the rest of the season.
Inter are winless in eight Serie A games, drawing all of their last five, and have fallen 15 points behind leaders Napoli.
"It seemed like it was going to be our year," said Ronaldo. "You can't go on questioning everybody, from the players to the coach, every year.
8 - Inter Milan have equalled their longest winless streak in their Serie A history (eight games), recorded on five occasions – the latest in May 2017. Fasting. #InterCrotone— OptaPaolo (@OptaPaolo) February 3, 2018
"You've got to believe in a project and give it the time it needs to work. What Inter did in the first two months of the season can't have been a fluke.
"Everybody was saying how Spalletti was their best signing. I tend to agree more with what 'my' president [Massimo] Moratti says: if he is as good as he definitely is, then now is the time for him to find the key to get certain players – I'm not naming names – back to playing at certain levels, even if it means he has to change something."