Vardy, whose release clause was triggered by a £20million bid from the north London club earlier this month, is currently on international duty with England at the European Championship in France.
The 29-year-old refused to make a decision on his future before leaving for the tournament and is expected to resolve the matter on his return.
Leicester have grown increasingly confident that Vardy, who scored 24 goals in their remarkable Premier League title-winning campaign last season, will stay.
Wenger, the Arsenal manager, has now dampened the speculation surrounding the deal further by implying that the former Stocksbridge Park Steels striker will stay at the King Power Stadium.
“Jamie Vardy is, at the moment, at Leicester and on what I know, he will stay at Leicester,” he said in an interview with Japanese television.
Vardy has repeatedly said that he is only currently thinking about his commitments to England and that the uncertainty over his future is not a distraction.
“It’s been easy to shut that out,” he told a press conference on Saturday.
“I’m here to concentrate and focus on England and that’s all I’m going to be doing and now we’ll just get back on that training field and focus on the next match.”
Vardy has been left out of the starting line-up for both of his country’s games at the tournament so far, despite clamour from supporters for Roy Hodgson to select him from the off.
The 29-year-old came off the bench to score England’s equaliser in a 2-1 win over Wales on Thursday.
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