Rabiot has been out of sorts in Paris since the end of last year, not featuring for the French champions since mid-December.
The homegrown talent was frozen out by the club after disputes over a new contract reached boiling point.
It means the midfielder can join any team for free this summer after bitterly seeing out the final year of his deal in the French capital.
And the Daily Mail claim Rabiot’s representatives have “offered” the services of their client to Manchester United.
Rabiot was managed by his mother until February, when he reportedly fired her for a more savvy transfer market operator.
Manchester Evening News report that United were already monitoring Rabiot and feel they can lure him to Old Trafford, despite failing to qualify for the Champions League.
The article claims Rabiot is seen as an “ideal option” for Solskjaer given his Champions League experience and international pedigree, owning six France caps.
Left-footed, the 24-year-old is adept on the left side of a three-man midfield, although this is Paul Pogba’s preferred position.
He has been touted as a long-term replacement for Nemanja Matic but is not a holding midfielder by trade.
PSG are expected to welcome departing United midfielder Ander Herrera on a free this summer which will instantly ease the loss of Rabiot.
Real Madrid and Barcelona are also reportedly interested in Rabiot – and Arsenal manager Unai Emery wanted his former player in January, and may still.
Speaking in January on the Arseblog podcast, BBC sports reporter David Ornstein said: “There are credible reports that Arsenal will now try to come back in for Rabiot.
“There are people within Arsenal who are very keen that they sign Rabiot or that they make the concerted effort. He’s very highly admired.
“There are some complications around him and the people you have to deal with, if you want to do a deal for him, and his salary demands.
“But I think that’s certainly a one we should keep an eye on.”