Football Italia says Napoli are interested in Lucas, 25, as a back-up option if Simone Verdi decides not to make a mid-season switch to Naples from Bologna.
The Serie A leaders have also been linked with a move for Barcelona forward Gerard Deulofeu if their pursuit of Verdi does not pan out.
Lucas revealed over the weekend that he is not part of PSG coach Unai Emery's plans for the future and admitted that he is keen to play in the Premier League.
The former Sao Paulo winger has only made five Ligue 1 appearances for the French giants this season and was an unused substitute in the club's 1-0 win over Nantes on 14 January.
"Is there a chance that I stay this winter? I do not think so," Lucas was quoted as saying by ESPN after the game against Nantes. "With what the coach has said, it looks like this is the end of my Paris story.
"I have offers but I cannot talk about them. I like English football very much, it is truly one of the best leagues in the world.
"I have always said that I want to stay in Europe – I still have things to achieve here."
The Football Italia report says PSG will only allow Lucas to leave on loan, but with an obligation to make the transfer permanent if the Brazilian makes a certain number of appearances before the end of the season.
United boss Jose Mourinho is in the market for a winger after he missed out on Inter Milan's Ivan Perisic in the summer, with Lucas providing the added benefit of not being cup-tied in the Champions League as he did not feature in any of PSG's six group games in the competition.
United have also been heavily linked with a January move for Arsenal forward Alexis Sanchez. It is unclear if the Old Trafford club will continue to pursue Lucas if they manage to land Sanchez.