PSG have been long-time admirers of Rashford, who has a year left on his United contract, although the club have the option to extend that by a further year.
Rashford has recently spoken of his desire to sign a new contract.
However, news of the meeting will start to focus minds around the long-term future of the 24-year-old, whose form nosedived last season, reports BBC Sport.
PSG transfers chief Luis Campos is a fan of Rashford and is driving the move.
Rashford lost his place in Gareth Southgate's England squad and against Brighton on Sunday, failed to take a clear chance which, if it he had found the net, may have stood following a VAR check given a debatable offside decision was eventually made.