But the Chelsea target's absence yesterday was due to a missed flight and a late replacement from Argentina, which Inter were quickly informed of, according to Sky Sports.
A number of high-profile players have been linked with moves to Stamford Bridge this month as the club look to fix their forward problems.
Gonzalo Higuain has reportedly agreed terms with the Blues and could become a Chelsea player today.
But Inter hotshot Icardi, 25, is apparently Abramovich's No1 target.
Chelsea will need to fork out £90million to meet his release clause – and act quickly as Inter are frantically trying to tie him down to a new deal.
Icardi finished last campaign as Serie A's top scorer with 29 goals and already has 13 in all competitions this season.
His dazzling form has also attracted interest from Real Madrid.
Icardi is out of contract in 2021 but Inter are hoping to extend his current deal.
Last month, Inter chief Piero Ausilio said: "The renewal of Icardi? On our end, we still hold on to what has been said in recent months. We are happy with Icardi, of what he is giving on the field, and he always takes responsibility.
"His agent? She knows where to find me, in the office or on the phone. I say things how they are, Icardi received a contract two years ago and signed it.
"The most recent proposal was two months ago, which he received but it was not accepted. This doesn't mean a dead end, we want to continue the negotiations."
Should Chelsea manage to bring in Icardi, it would open the door for Alvaro Morata to join Sevilla on loan.
The Spanish striker, who picked up a hamstring injury in last night's 1-0 Carabao Cup semi-final defeat to Tottenham, has scored just five Premier League goals this term.
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