The Brazilian international made 55 appearances for the French champions last season, but only played the full 90 minutes on 10 occasions and was left out of the starting XI for a number of high-profile matches.
It is understood that Liverpool are keen on bringing the 23-year-old to England, but Lucas has insisted that he wants to remain with the Ligue 1 champions, who are now under the management of Unai Emery.
"I keep the same mentality to help the team. I want to play and start, as all players do. I'm not different," Lucas told L'Equipe. "I'll give everything to start. There will be competition but I can help the team a lot.
"I'm happy here. I love the club and Paris. I have said I want to stay here and write my story, but it also depends on the club. If they want me to stay, I will stay."
Lucas, who almost joined Manchester United from Sao Paulo in 2013, scored 13 times in all competitions for PSG last season, including nine in the league.