United are among the European clubs interested in the Frenchman, after he ran down his contract at Paris Saint-Germain.
The central midfielder is available on a free, which means that he has his pick of interested teams to decide where to continue his career.
United do want to sign the 24-year-old.
Tottenham and Arsenal are two other teams who could be interested, given their lack of transfer fund availability to strengthen their teams.
But United could blow their rivals out of the water with their wage and signing bonus offer to Rabiot, if they see him as a "must-sign" player this summer.