The Argentina striker's contract, which expires in 2021, is said to contain a release clause of €112 million (£100m/$130m) that is applicable only to foreign clubs.
Real Madrid were linked with a bid, but their interest did not materialise, even after they sold Cristiano Ronaldo to Juve for a fee close to Icardi's clause.
Now, Icardi's wife and agent Wanda Nara has suggested he could have joined the Serie A champions had they failed in their efforts to bring Ronaldo to Turin.
However, she suggested the 25-year-old's wish was always to remain at San Siro.
"The only contact Mauro has had with Juventus are the seven goals he's scored against them," she told TV show Tiki Taka.
When pressed on whether Juve considered signing Icardi, she replied: "Certainly. They took Cristiano Ronaldo, who was their primary objective. Certainly, Mauro could have been an alternative.
"Mauro made it clear immediately what his choice was. It's obvious a forward like Mauro is wanted during a transfer window.
"If a president calls me, I have to do my job. If they call me, I answer, but the final decision is up to Mauro."
Nara also said she met with Napoli president Aurelio De Laurentiis and thinks their interest in Icardi went as far as an offer being made to Inter.
"Yes, I met him. He's a very good person," she admitted.
"The interest in Mauro was there. They even made a proposal to Inter. The player then decides."