Icardi was stripped of the club captaincy and dropped from the first team in February and has been widely linked with a move away from San Siro.
And now club chief Beppe Marotta says he is prepared to let Icardi go for the right fee and has confirmed his interest in bringing Lukau to Serie A from Manchester United.
"We’re ready to negotiate with anyone who wants to buy Icardi, respecting the value of this player," he told Sky Sport Italia.
"[Edin] Dzeko and Lukaku are very interesting players who have different characteristics. They are both targets and I won’t deny that.
"As for [Nicolo] Barella, we want to complete this transfer. It’s only right that Cagliari state their asking price. We want to bring him here because he encapsulates our values.
"He’s also Italian and we think it important that an Italian club has a solid core of homegrown players to achieve important results."
When asked about whether Icardi and his agent/wife Wanda Nara met with Juventus chief Fabio Paratici, he plead ignorance.
"I heard about this alleged meeting through the media, but I have nothing concrete to tell me if they met or not. We wouldn’t even have felt the need to disguise it."
Inter are currently rebuilding following the big-name appointment of Antonio Conte as manager.