Makelele has been strongly linked with a move to the Parc des Princes in recent weeks, with PSG coach Paul Le Guen confirming his interest.
The 35-year-old is understood to be travelling to France to have a medical ahead of a proposed return to Ligue 1 football.
The former Real Madrid anchor man has 12 months left on his current contract at Chelsea and has previously suggested he would be keen on an extension.