The 19-year-old has been linked with moves to Manchester United and Inter Milan this summer after breaking into Brazil's national side.
However, Les Parisiens now appear to be in pole position for his signature, Sao Paulo vice-president Joao Paulo de Jesus Lopes has confirmed.
"We have been probed by PSG about Lucas," Lopes told Le 10 Sport. "Leonardo has a very good relationship with Sao Paulo, but for now nothing is definite.
"The possibility exists but it is down to the player's interests. The policy of Sao Paulo is to follow the desires of the player. If the player wishes to leave, Sao Paulo will not create any obstacle - but we must receive a proposal that is appropriate.
"It's a financial issue. Paris Saint-Germain is a big club in European football and if the player's interests and also the club's are met, I do not see why it would not happen."
Moura is currently on duty with Brazil at the Olympics.