The Argentinian striker is currently in limbo at Inter after being dropped from the squad and stripped of the captaincy.
It is believed to be over his delays in signing a new contract with the Italian giants.
His current deal ends in the summer of 2021.
That has alerted Chelsea, who only have a deal for Gonzalo Higuain in place until the end of the season.
Icardi would provide a younger and cheaper option, with the striker believed to be available for just £34million.
But according to AS, there is set to be a fair amount of competition for the 26-year-old goalscorer.
Napoli and Juventus are also eyeing Icardi, with Inter preferring to thrash out a deal with Juve above all else.
That is due to the positive working relationship between the two clubs due to Inter CEO Beppe Marotta previously being a director at Juve.
Icardi's wife and agent Wanda said last month that Inter were yet to offer the striker a new contract.
The 32-year-old TV host and model has been openly critical of Inter's transfer policy, and has even taken a swipe at performances on the pitch.
Chelsea made their interest known during the past transfer window as they looked for a replacement for Alvaro Morata, who left for Atletico Madrid on an 18-month loan deal.
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