Tatum, 35, earlier said he finds Bomer's eyes beautiful, saying he "gets lost" in them.
"I don't know what they are made of outside of dreams and rainbows and amazingness," Tatum joked.
Asked about his reaction to the compliment, Bomer, 37, said Tatum's generosity didn't end with mere compliments.
"I mean, obviously, I blushed," Bomer said.
"Knowing Channing, and what a kind soul he is, I guess when you're the most handsome man on the planet - and probably the most desired man on the planet - you have the security to give those kinds of compliments It was great. It made my day, of course! I and the rest of the world feel the same way about him.
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