Various reports in England claim that the 'Red Devils' are weighing up a move for the Brazilian, who was previously of interest to Sir Alex Ferguson back in 2012.
Moura has not started a single league game for the Parisian side so far this campaign and is thought to be available for around £25m as PSG try to offload players in order to comply with Financial Fair Play.
United are known to be keen on adding a winger to their squad, having seen a move for Inter Milan's Ivan Perisic collapse last summer.
Whilst Moura does feature in United's thinking, Jose Mourinho is thought to have other targets in mind as he looks to strengthen his squad this month.
Nevertheless, French source 'Telefoot' rates United as favourites to sign the player, though there is a potential stumbling block in the deal, with United thought to favour a loan, rather than a permanent switch.