The England international was then expected to undergo a medical with the North London club as a move to the Gunners looked imminent.
However, Vardy, currently with the Three Lions at Euro 2016, is believed to have delayed a decision over his future until England's participation at the competition in France has ended (The Guardian).
Despite finishing 10 points above second-placed Arsenal, Leicester are not a bigger club than Arsenal, and joining Wenger's side would be a significant step up.
As a result, former Leeds United defender Mills has joked that he would have walked to North London to join the club if he heard they wanted him, and says that the French boss, 66, will have been irked by the delay over Vardy's future.
Speaking to BBC Radio 5 Live, Mills said: “I would have walked down the M1 to Arsenal!
“I find it bizarre. If you’re agent’s speaking to Arsenal, the first question is: ‘Do you want to go to Arsenal?’
“It should be done and dusted. To turn around and say: ‘I’m going to think about it’… I don’t think Arsene Wenger will like that.”