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The legendary frontman, who performed with Lambert during the Idol finale, told Extra that he is a big fan of the 27-year-old singer.
"Adam was fantastic. What a powerful and attractive man he is," said Simmons.
"He can come on tour whenever he'd like. Of course, he'd have to put his armour on because the fans, especially the KISS fans, take no prisoners. You gotta go big, you gotta be strong. You gotta be a rock, baby!"
When told about the offer, Lambert replied: "That'd be such an honour. I had so much fun - to perform with KISS, I would love that. What a wonderful compliment... That was very, very nice of him."
Lambert is scheduled to join his fellow Idol finalists for a 50-date tour of the States this summer, kicking off in Portland, Oregon on July 5.
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