The Parisian side have endured a difficult season following the resurgence of Monaco under Leonardo Jardim, and they now find themselves three points behind the league leaders, who also have a game in hand over Les Rouge-et-Bleu.
"As long as it's mathematically possible, we're going to do everything to play for the title right to the end," Maxwell told the club's official website.
"The aim is to play and honour the Paris Saint-Germain shirt right to the finish. It's been a season with ups and downs, but it's a season which has allowed us to learn.
"We have to know how to value what we have done and improve so we can win trophies again."
PSG's final two Ligue 1 fixtures see them face Saint-Etienne and Caen.