The Blues are in the market for a striker this January following the failings of Alvaro Morata.
The Spanish striker seems beyond the point of no return at Stamford Bridge, with a weekend brace over Nottingham Forest even being overshadowed by a shocking, but offside, miss.
Manager Maurizio Sarri has eventually followed the fans and lost faith in the 26-year-old, who arrived for £58million last summer, while deeming Olivier Giroud not good enough to regularly lead the line.
While the club seek a destination to offload Morata, they are upping the search for a replacement.
The Mirror are reporting that Icardi is the top target and Abramovich is willing to supply a fitting warchest to land the Italian.