United have already made enquiries into signing the Argentina international, as reported by the Sunday Mirror in September, with chief executive Ed Woodward making it known to the player's management team that if and when he decides to leave Italy, Jose Mourinho wants him at Old Trafford.
Spain's big two are also among his admirers, however. According to Mundo Deportivo, Real Madrid president Florentino Perez has earmarked Dybala as their next 'Galactico' signing. The same publication reported in July that Barcelona have a first option to sign him for around €120m (£110.4m, $143m) thanks to a special clause insisted upon by the player when he signed a new contract in April.
Dybala is only seven months into that new deal with Juventus managing director Giuseppe Marotta recently claiming the player has informed the club he wants "to tie himself to our club for life".
The player's latest comments made to France Football would suggest otherwise, however.
"I don't know if I will be at Juventus for life and I can't even sat that this will not be my last year in Turin," he told the publication, the Mirror report.
Dybala played alongside Paul Pogba in Turin with the France international doing his best to excite United fans by bringing back the 'Agent P' moniker in a recent interaction with the Argentine star.
Pogba first referred to himself as 'Agent P' during the summer transfer window on social media in pictures with good friend Romelu Lukaku, who would later complete a move to Old Trafford for £75m.
Pogba teased United fans again last week, signing off with that name after wishing Dybala a happy birthday on Instagram.
Dybala now admits he misses playing alongside his former teammate and Dani Alves, who left Juventus to join Paris Saint-Germain in the summer.
"I must admit I miss Dani Alves and Pogba," he said. "Alves had an amazing vision and is really self-confident, he is one of the best players I have ever seen. Pogba is a friend of mine, we were on very good terms on and off the pitch."