"I've had the privilege of meeting him a couple of times," the Briton told Sky Sports television at the Azerbaijan Grand Prix.
"He asked me to go and train with the team, which I have not managed to do yet, but he was always really welcoming and it was cool to meet 'our team's' boss."
Hamilton, who said he had supported Arsenal since he was five, admired Wenger's commitment to the North London club over more than two decades.
"The loyalty which he has shown through all the ups and downs, through outside individuals saying positives and negatives, but to stay true to your values and continue to strive for what you believe in I think has really been awesome," he said.
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Wenger is leaving Arsenal at the end of the season, with the club yet to name a replacement.
Hamilton is out of contract with Mercedes at year end but has said that he and the team remain committed to each other although a new deal, expected for months, has yet to be announced.
"I've made it very clear, and they've made it very clear that they want to continue so it's quite an easy thing," he said in Baku.
"I don't... have that personality to say 'I'm definitely going to be with them next year' and then not be with them next year so it is just about finalising and signing off."
(Reporting by Alan Baldwin, editing by Sudipto Ganguly)
