The Croatian joined from Hadjuk Split in 2011 and has played every minute of league football this season as Claudio Ranieri's side attempt to challenge Paris Saint-Germain for the Ligue 1 title.
Argentina goalkeeper Sergio Romero has failed to usurp Subasic since joining on loan from Sampdoria, although the cash-rich club are thought to be weighing up a deal for Barcelona's Victor Valdes at the end of the season.
"I want to stay at Monaco next season," he said. "Whatever happens I want to go here."
Subasic has conceded just 17 goals in 24 league matches this season, but is determined to improve further as he looks to become Croatia's first-choice keeper leading into the FIFA World Cup in Brazil later this year.
"This is a good season for me, but it is not over yet," he said.
"I have to continue like this. (Stipe) Pletikosa is the number one selection. He is the vice-captain, he has experience. I'm number two, I wait my turn."
