The Brazil born-winger is an Italian citizen - so work permits would not be an issue if either club sought to do a deal. And United and Arsenal are both interested in bringing him to the Premier League, although Shakhtar Donetsk are also monitoring developments.
The 21-year-old moved to Verona from Italian lower league side Sambonifacese in 2011, and he's quickly become one of the club's star players.
Verona sit third in Serie 'B' - the Italian second tier - and Jorginho has played a key role as they push for promotion to the top flight, making 24 appearances so far this season.
The report claims Arsenal, United and Shakhtar are the main parties competing for his signature, and although the winger has three years remaining on his Verona contract, he could be available for a fee in the region of £6m.
Shakhtar Donetsk have a number of Brazilian players on their books, and the Ukrainian club have been linked with a move for Jorginho.
The reigning Ukrainian champions have 10 Brazilian players in their first-team squad, and recently sold Willian in a big-money move to Russian club Anzhi.
Arsenal were linked with a move for Jorginho in the January transfer window, after the Gunners' Italy-based scout Tony Banfield give him a glowing report.
The Metro claimed Banfield called Wenger personally to convince him to sign the winger, but a deal never materialised before the deadline.
During the January window, Jorginho was also linked with the likes of AC Milan and Napoli, but it now seems United, Arsenal and Shakhtar will battle it out to secure a summer deal for the Brazilian.