According to The Sun, the Red Devils manager Jose Mourinho has identified the Brazil international as a top target and is desperate to complete a deal that will see his side bring the 25-year-old to Old Trafford on a loan deal before the end of this month.
However, PSG are unwilling to let their player leave the club, if it is only a loan deal. They want to have an agreement, which will then see the 20-time champions of England sign him for £40m ($54.4m) after the loan deal.
Moura was wanted by United in 2012, while he was at Brazilian club Sao Paulo. Their former manager Sir Alex Ferguson was keen on securing his services six years ago. However, the deal did not take shape as he snubbed the Old Trafford club for PSG.
Chinese Super League side Beijing Guoan are also interested in bringing the South American attacker to the Far East. However, the player has set his sights on playing for another top club in Europe.
The former Sao Paulo attacker will be open to the idea of swapping PSG for United, if a deal can be agreed between the two clubs. He has made 212 appearances for the French capital club, scoring 44 times in the process and winning four league titles.
However, Moura has seen his first team opportunities being limited at Parc des Princes. He has not started in the league or the Champions League for Unai Emery's side this season and has made only two starts in the cup competition.
PSG signed Neymar from Barcelona for a world-record fee in the summer. They further bolstered their squad by signing Kylian Mbappe on loan from AS Monaco. The duo's arrival and having Angel Di Maria and Julian Draxler in the squad has seen Moura drop further down the pecking order.