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The Argentine striker has been in sensational form this season and is being targeted by numerous top clubs.
Real Madrid are understood to be extremely interested in signing Icardi, but they are yet to make a firm offer.
It’s understood that Icardi’s agent Wanda Nara, who is also his wife, has received the massive proposal.
Inter are highly likely to reject Chelsea’s offer, with the player believed to have an £80m release clause in his contract.
Nara recently revealed she was confident Icardi will renew his current contract at the San Siro, but Chelsea’s bid potentially changes things.
Icardi started his career in the youth system at Barcelona before moving to Sampdoria, where he began his professional career.
He joined Inter in 2013, and during the 2014/15 season he was the joint winner of the top scorer award in Serie A.
Icardi made his senior international debut for Argentina in October 2013.