Maxwell joined PSG from Barcelona in January 2012 and is currently under contract with the French champions until 2015.
The 32-year-old, who scored in the weekend's win over title rivals Marseille, is enjoying his time with PSG and would be prepared to discuss a new deal.
"It would be fantastic to finish my career at PSG," the left-back told a press conference. "It is my dearest wish to continue my career here.
"Finishing at Paris would be spectacular, so why not? It will soon be the right time to see what the club wants."
Maxwell also has his sights set on representing hosts Brazil at next summer's World Cup after only making his international debut against Switzerland in August.
He added: "This is a dream come true. I started to lose a little hope. Receiving my call-up has been a very pleasant surprise. It is now three times in a row, so I'm very happy and motivated.
"But I have to work here to hope to be called again. Playing the World Cup at home is fantastic. It is the dream of every player."