The France international’s contract in the French capital expires this summer and he has been linked with Premier League sides Liverpool and Arsenal.
However, El Mundo Deportivo reported on Thursday that the 24-year-old already has an agreement in place to join the Merengues at the end of the season.
Madrid coach Zinedine Zidane is said to be keen on securing the services of the midfielder as he looks to revamp his squad in the summer after a disappointing campaign.
Real Madrid were knocked out of the Champions League by Ajax at the last-16 stage and are third in La Liga, 13 points behind leaders Barcelona.
Rabiot hasn’t featured for PSG in four months, with the Ligue 1 leaders refusing to play him while his contract situation remains unresolved.
As things stand, he will leave the club on a free transfer when his deal expires on 30 June.
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