The 23-year-old PSG midfielder will soon be out of contract in the French capital and a number of Europe's top clubs are tracking him.
Tottenham, Chelsea and, most prominently, Barcelona have all been heavily linked with a serious move for Rabiot but now United have entered the fray, say The Sun.
A contractual dispute means Rabiot hasn't played for PSG since December 11, so a summer exit seems inevitable – although reported wage demands of £200,000 per week may be off-putting to potential suitors (hello there, Daniel Levy).
Paul Pogba looks set to remain at Old Trafford after some fine form under Ole Gunnar Solskjaer, but United still lack creativity in midfield beyond the mercurial Frenchman.
Rabiot has made more headlines for his off-field demeanour than on it over the last 12 months, however.
His failure to agree a new deal at the Parc des Princes is one thing, but the midfielder was widely criticised for refusing to be on France's standby list at the 2018 World Cup.
Most recently he was suspended until the end of month after being spotted in a nightclub following PSG's acrimonious Champions League exit to United.
Paris Saint-Germain sporting director Antero Henrique fumed: "I find his attitude and lack of professionalism towards the club, his team-mates and supporters unacceptable. I would like to point out that until June 30, he remains a member of our squad."
