The 26-year-old could be one of the most expensive acquisitions in this summer’s transfer window – and indeed, if United land him for the £50m quoted by the Daily Mirror, he would become their record signing.
The key rivals for his signature at this stage are Real Madrid and Chelsea, the paper adds, and although Cavani has a £54m release clause, since no club has yet matched that Napoli may be prepared to let him go for slightly less than that.
Now Paper Round is naturally a cynical sort, so whether United will spend twice their previous record in the Glazer era on a single player remains to be seen – especially if the man asking for the money is Moyes, rather than Sir Alex Ferguson.
Whether they need another striker rather than a midfielder is also a factor.
But the report suggests that Wayne Rooney’s sale this summer would offset at least some of the Cavani fee on one hand, and on the other the deal for Barcelona midfielder Thiago Alcantara would not be affected.
Speaking of Rooney, The Sun picks up on a link with the forward and a move to Barcelona.
First of all, the 27-year-old will have showdown talks with Moyes over his future – but if those end with him being surplus to requirements, the Catalans would reportedly pounce, seeing his versatility and work rate as useful additions to the squad.
A £25m deal for Rooney, as well as offloading his £250,000-a-week wages from the accounts, would certainly help the Red Devils commit to the Cavani move.
The Daily Mail has also got word of United’s bid for Cavani, but cites reports from Italian radio that Chelsea have agreed a £49.3m deal for his sale.
The player’s agent, Claudio Anelucci denies that line, however, saying: “There is nothing closed with Chelsea .”
In an interesting line in the same paper, Arsenal appear to be getting cold feet at the prospect of signing Marouane Fellaini.
It is believed that the Everton man favours the move to London, but wants his wages increased to £100,000 a week, and with a release clause of £22m, a long-term deal for the 25-year-old could commit the Gunners to around £50m worth of expenditure on his deal.
There’s a bit of doubt across the back pages, meanwhile, about the future of Isco. The Sun say that Manchester City have missed out on his signature, with Real Madrid set to confirm his arrival imminently.
But the Daily Star say all is not done yet – and that manager Manuel Pellegrini has made a personal plea in a last-ditch bid to sign him.
Their spell working together at Malaga was believed to give City the edge in the £30m bid, but reports in Spain suggest Isco will be unveiled at the Bernabeu this week.
The Mirror says a midfield ace is on the way to the Premier League, however, with Paulinho reportedly set to join Tottenham in a £17m transfer.
The Brazil international is expected to link up with Spurs after the Confederations Cup, with the following quotes from the player taken as proof of his intent:
The 24-year-old said: “It is a pleasure to be linked to such a great club like Tottenham. They have a reputation as one of the great clubs in England who play exciting, attacking football which suits my style.
“I couldn’t turn them down if they made me an offer. It would be a fantastic opportunity to play for Tottenham.
“I feel I am ready to experience football at the highest level in Europe and the opportunity to play in England is a dream.”
Sticking with the Mirror, Paolo di Canio is clearing the decks at Sunderland for a summer spending spree.
The paper reckons that Di Canio will use the money for as many as 10 new players and the team will be unrecognisable from last season’s.
One face could be familiar to Premier League followers, however – Jozy Altidore, the former Hull striker now at AZ Alkmaar, is a key target.
The Daily Express, meanwhile, carry reports that Nathan Redmond could be a Swansea player after Birmingham accepted a £2.5m bid – but Norwich have also had an offer accepted.
And also in the same edition are reports that Liverpool target Henrikh Mkhitaryan has rubbished reports linking him to Anfield.
The Reds were optimistic of tying up a £22m deal for the midfielder, but he took to his Facebook page to say he was focused on life at Shakhtar Donetsk.
"I am happy to see that people show keen interest in my career,” the Armenian said, “but I would like to ask all not only to refrain from making comments but also to prevent the spread of unverified and false information.
"I am not meddling with these affairs. If have a contract with a club, I just fulfil it."