The striker is in limbo at his current club Inter Milan after being stripped of the captaincy and dropped from the first team squad.
It is believed to be linked to an ongoing contract dispute – his current deal ends in 2021.
Icardi's wife and Wanda said last month that Inter were yet to offer the striker a new contract.
Reports claimed San Siro chiefs were stalling on Icardi's £170,000-a-week wage demands.
This will no doubt alert Chelsea, who are believed to be long-term admirers of the 25-year-old striker.
But according to Spanish newspaper Marca, one place he won't be heading is to the Bernabeu.
It is reported that Los Blancos ditched plans for a January swoop because of "Wanda's behaviour".
The 32-year-old TV host and model has been openly critical of Inter's transfer policy, and has even taken a swipe at performances on the pitch.
And seemingly Real Madrid are not interested in making headlines for the WRONG reasons.
That will open the door for Chelsea to plot a move for the Argentinian international this summer – with the striker department still an area of concern.
And though Icardi's future remains up in the air, Inter fans seem pleased that the captaincy has gone to experienced keeper Samir Handanovic.
As does Icardi's team-mate Marcelo Brozovic, who liked a photo on Instagram showing that Icardi was no longer captain.
One wrote: "Great decision. Finally someone saw something wrong with assigning Icardi to be our captain while he can't captain his wife."
Another said: "Great decision, no more s*** drama from our captain."
A fellow user posted: "Icardi leaving?"
But Icardi's own sister believes it is Wanda's fault for Icardi's Inter omission.
As quoted by CN24 and cited by Sport Witness on Twitter, Ivana claimed that if Mauro had "a serious person behind him", none of this would have happened.
She added: "My poor brother, why does he continue to allow this? An Inter they don’t allow these attitudes."
Last month Ivana had claimed Wanda "has s*** for brains" after it was reported that she keeps calling ex-husband Maxi Lopez, who she left for Icardi in 2014.
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