The Brazil international has not started in the Ligue 1, nor has he featured in the Champions League this season. He has only started in two games, both of which came in the cup competitions.
According to the French publication Le Parisien, Moura has no desire to continue with his current employers or in France beyond this month. He is not looking at swapping PSG for AS Monaco or Lyon.
He has set his sights on making a switch to the Premier League. Moura's representatives believe a move to England would be ideal and they want their client to join Jurgen Klopp's side as a replacement for Philippe Coutinho.
The former Inter Milan man left Anfield and completed a switch to Barcelona for a fee of around £142m ($192.6m). The PSG wideman was a transfer target for the Merseyside club two years ago, but no negotiations took place between the two clubs.
Moura has dropped further down the pecking order after the arrival of Neymar and Kylian Mbappe last summer. Emery has already said that his side will allow the wideman to leave due to lack of opportunities.
"Some players who play less, maybe they can be protagonists of another team because they are good players and do not have the opportunity to play here, like Lucas Moura or Hatem Ben Arfa," Emery explained.
United's former manager Sir Alex Ferguson was keen on signing him before he moved to Parc des Princes in January 2013. The Red Devils are currently managed by Jose Mourinho and the Portuguese tactician is keen on bringing him to Old Trafford.
Moura is also attracting interest from the 20-time champions of England and is open to the idea of swapping PSG for United. However, the Red Devils will only take the 25-year-old on loan in January.
This idea has been rejected by the PSG and the player as they are looking for a permanent transfer. The same report also claims the French capital club are looking at a fee of around €40m (£35.84m, $47.7m) to part ways with Moura.
Brazilian publication Globo Esporte claims Moura's employers are looking to balance the books in order to comply with Uefa's Financial Fair Play (FFP) regulations following the signing of Neymar for a world-record fee of €222m.
Thus, PSG have ruled out the possibility of allowing Moura to go out on loan this month. United are in negotiations with Emrey's side for the winger and believe a bid of around €25m would convince them to sanction his sale to the Red Devils after the player has already agreed to join them.
It should be seen whether Liverpool can beat United in signing Moura as the latter is still hoping to sign him on a loan deal.