Chelsea's $105 million signing Morata endured a poor first season in the Premier League, hampered by injuries and inconsistent form, and was this week spotted in Milan meeting with Juventus director of sport Fabio Paratici - fuelling speculation of an early exit from Stamford Bridge.
However, Il Messaggero and Cadena Ser report Chelsea are keen to use the Spaniard as part of a swap deal with Inter for Icardi.
The mammoth deal being touted is Morata plus €35-40 million for Inter's Argentine captain.
Icardi enjoyed a stellar campaign, ending as top scorer in Serie A on 29 goals (joint with Lazio's Ciro Immobile), as the Nerazzuri secured a top four finish and a return to UEFA Champions League action for the first time in six years.
He has been prolific in front of goal since joining Inter, scoring 107 goals in 182 matches, and has a €110m ($170m) release clause in his contract - although that expires on 15 July this year.
Morata and Icardi are both 25 years old and neither one has been selected for the 2018 FIFA World Cup squads of their respective nations.
