Rabiot, 24, is a free agent this summer after failing to sign a contract extension with PSG.
He hasn't featured since the start of December and has since been suspended for his antics after the Champions League defeat to Manchester United.
Liverpool and Arsenal have been credited with an interest although Barcelona appeared to be in pole position before PSG criticised the conduct of the La Liga champions.
That put Real Madrid on alert and reports in France suggest a move is in place.
Zinedine Zidane is a long-term admirer of Rabiot and considered taking him to the Bernabeu before his departure last summer.