United first made moves for the 25-year-old way back in 2012 before PSG flexed their new found financial muscles at Sao Paulo, there had been rumours of a possible £20m bid made from Old Trafford but it is believed that no firm offer has yet to be made.
And after seeing their player restricted to just 72 minutes of Ligue 1 football this season, Lucas' camp - led by agent Wagner Ribeiro - have begun the search for a Premier League club willing to end his PSG exile and reinvigorate his push for a place in Brazil's World Cup squad.
Jurgen Klopp is in the market for attacking reinforcements following Philippe Coutinho's £142m move to Barcelona and Moura has been linked with a move to Anfield in the past.
Moura directly contributed in 30 goals last season but this season, he has only warmed the bench under Emery.
Moura has fallen out of favour at PSG following the arrivals of Kylian Mbappe and Neymar in the summer.
GETTYLiverpool news PSG star Lucas Moura could replace Philippe Coutinho
United's former manager Sir Alex Ferguson was keen on signing him before he moved to Parc des Princes in January 2013.
Earlier in the week reports spread that PSG midfielder Lucas Moura has "agreed" a move to Man United.
However, United and PSG remain locked in talks as they aim to thrash out an agreement over the fee for the winger.
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.
Nonetheless, PSG representatives don't seem to be interested in such a deal, as they prefer to sell the player outright.