According to James Ducker of the Daily Telegraph, the Gunners could demand as much as £25 million to do a deal for the Germany international in the January transfer window, even with his contract due to expire at the end of the campaign.
But Mourinho and United are said to be ready to capitalise on Ozil's reluctance to extend his stay at the Emirates Stadium and strike a deal at the end of the campaign when his contract has expired.
As Ducker noted, when asked about a possible swoop for the former Real Madrid man on Friday, the United boss said "no comments." Samuel Luckhurst of the Manchester Evening News read between the lines, though:
Although Ozil has divided opinion during his time at Arsenal, losing him for nothing would be a huge blow for the club. Meanwhile, picking him up on a free would be a major coup, even for a team of United's calibre.
The German has the guile and grace to decide a game for his side when he's at his best. It's something Mourinho will be well aware of, having managed Real Madrid while Ozil was at the club.
In terms of technical play, there aren't many footballers on the same plane as Arsenal's No. 11. His composure in possession, vision and ingenuity are second to none at times, making him integral when trying to unpick a massed rank of defenders. That's a challenge teams like the Gunners and United face on a regular basis.
As we can see here, courtesy of WhoScored.com, Ozil has been in exceptional form for Arsene Wenger's side as of late:
Per Ducker, the Arsenal boss has admitted in the past there is a possibility the playmaker could be sold midseason, although losing him would leave a massive hole in the final third.
Alongside Alexis Sanchez, who is also out of contract at the end of 2017-18, he's the crucial influence at the top end of the field for the Gunners. Arsenal supporters might prefer to keep Ozil around for the rest of the campaign rather than take the £25 million a team may offer.
Jack Pitt-Brooke of The Independent hailed just how much of a joy the 29-year-old can be to watch when he's on it:
According to John Cross of the Daily Mirror, Barcelona are also interested in doing a deal for Ozil. Cross suggested the Blaugrana would be ready to pay the German a staggering £350,000 per week too.
The prospect of linking up with Mourinho again could be appealing for Ozil, and at the hub of his Red Devils side, the 29-year-old be able to weave his magic upon solid foundations. Either way, it appears likely this season will be his last in Arsenal colours.