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.
Valdes was linked with a move to Stade Louis II before the current season, though he committed the final year of his contract to Camp Nou.
The Spain international will leave the Catalan giants at the end of the season though, and will be available on a free transfer, though Subasic is not concerned about any potential rivals for his number-one spot.
"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."
Monaco currently lie five points adrift of PSG, with a trip to eighth-placed Bastia to come on Saturday.
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