The Blues are understood to be tracking the 21-year-old after being impressed by his fine Serie A goalscoring form.
Icardi is currently the Nerazurri’s top attacking threat and has notched 11 goals in 23 outings this term.
Chelsea were thought to be eyeing an end of season move for his signature, yet Atletico’s raid for him has pushed plans ahead of schedule.
The La Liga champions are believed to have offered Mario Suarez plus cash for Icardi, which may tempt Inter.
Jose Mourinho’s side could now have to up their game or risk missing out on the young forward.
Icardi is already a one-time Argentina international and has notched 19 goals in 40 appearances for Inter since joining the club from Sampdoria 18 months ago.