United had been confident of signing the Brazil playmaker until PSG made a last-minute offer.
The Qatar-backed French club are prepared to pay almost £36million and would wait until January to take him from Sao Paulo.
"Without doubt it would be much better for me to stay to help Sao Paulo until the end of the year," said the 19-year-old.
"I want to win a title before I leave, qualifying for the Copa Libertadores. If the deal is in January, I can do this for Sao Paulo.
"I can't talk about it," Lucas insisted after the 3-0 semi-final victory over South Korea on Tuesday night. "I'm focused on the national team.
"I can only say something after the Olympics. It's on the right path, (but) nothing is certain."