The Brazil international was previously linked with clubs such as Manchester United and Inter, but now appears to be on his way to the Ligue 1 giants
The attacking midfielder is continually being linked with a move to Europe, with Manchester United and Inter both keen to lure the 19-year-old away from his current club.
Nevertheless, United and Inter have no intention to meet Sao Paulo's hefty asking price for Lucas, thus allowing PSG to move into pole position in the race for the Brazil international's signature.
"I talked to Thiago Silva and Leonardo, they said many good things about the club, the project they are implementing there. Talks are well under way, but not done yet," Lucas stated to Globo Esporte.
"I will stay at Sao Paulo until the end of the year. I have always said that I want to win a title and qualify for the Copa Libertadores before leaving.
"If the transfer happens in January, I'll be able to do that for Sao Paulo. For now, I'm focused on the national team, though. I can only say something after the Olympics."
PSG currently have a maximum of four non-EU players in their squad, but they are hopeful that Milan Bisevac will receive dual nationality shortly, permitting them to add another player from outside the European Union to their squad either this summer or in January.