Despite this, American Kroenke has reiterated his desire to keep Wenger at the Emirates, noting specifically his ability to bring through young talent.
"Maybe it is one of those times when we have to work our way through, maybe with some young players," Kroenke said.
"Arsene has been really good at developing these guys, people like Alex Oxlade-Chamberlain and Jack Wilshere.
"Arsene's our man. As an owner, that's who we put our confidence in."
Kroenke also said it will be the Frenchman's decision with regards to when he wants to leave his post in North London
He added: "With Arsene, it's his decision and only he will know that.
"He still maintains himself in tremendous physical shape. You have to have stamina and energy.
"Arsene has great energy and that will always be his decision."
The Gunners currently sit 13th after six games of the Premier League season and travel to White Hart Lane for a showpiece game with Spurs on Sunday.