Both sides are expected to be in the market for a forward this summer to bolster their options up front.
The Gunners let Pierre-Emerick Aubameyang leave the club in January, while Alexandre Lacazette and Eddie Nketiah are out of contract at the end of the season.
At Old Trafford, meanwhile, Edinson Cavani’s deal is also up this summer, leaving incoming manager Erik ten Hag potentially short on strikers.
Dybala is expected to leave Juventus when his contract expires at the end of June, with the 28-year-old able to negotiate with foreign clubs over a free transfer.
Clubs in Italy and Spain are also said to have been in touch with the player’s camp as he looks unlikely to extend his stay with the Serie A outfit.
United interim boss Ralf Rangnick has already urged Ten Hag to sign two new strikers this summer.
Rangnick admitted the Red Devils are reliant on Cristiano Ronaldo, who scored his 23rd goal of the season across all competitions during United’s 1-1 draw with Chelsea on Thursday night.
‘We have to still be fair with the players,’ Rangnick said after the draw at Old Trafford. ‘We had quite a few other players scoring goals.
‘I remember, in my first 10 games, we had 10 different goalscorers. It is how many opportunities can we create and how many goalscorers.
‘Right now, we very much rely on Cristiano, he also showed a good performance when Chelsea were in possession. But there has to be a focus on bringing in a couple of new strikers for sure.’
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