The Dutchman’s attitude has angered Fulham manager Felix Magath, who revealed the keeper would leave Craven Cottage during the transfer window.
Stekelenburg has not featured in pre-season and lost his place in the starting line-up to David Stockdale.
“He’s a player that wants to leave and I’m not a manager who cares about players who don’t identify with the club,” Magath said ahead of their Championship opener with Ipswich.
“That was a problem last season. I told everybody you can stay here, you can work with me, I will work with you but if you don’t want to with me please leave.
“I don’t want to work with players who have no heart for the club.”
Stekelenburg, who was not selected by Louis van Gaal for the Netherlands World Cup squad, will now be given the opportunity to impress during his temporary spell in Monaco.
"I am happy to be a part of the project of the club,” the 31-year-old told their official website.
“I am going to give myself fully for my new club. I am a ‘technical’ goalkeeper. I like playing far from my goal and helping the team. "