Konate, signed from RB Leipzig in the summer, made his first Premier League start in Saturday's 3-0 win over Crystal Palace.
"Ibou is a top guy and an unbelievable player," Gomez said. "Look at his attributes, you can see how good he is.
"When I was younger I had Virg, but Ibou is already experienced, he's already a top player, he's played in the Champions League.
"It's just enjoyable playing alongside him, we both relish being young centre-backs trying to prove ourselves.
"We strive to push each other every day.
"It's a healthy environment. We're all really close. Everyone knows how close I am with Virgil, but I am with Joel as well.
"Maybe people don't see it because Joel is not on social media, but we are all very close."
Gomez will likely be rotating with Konate this season, but that doesn't faze the Englishman.
He continued: "It's healthy and we all need rotation as well. We've all had our injuries, and I think that [rotation] will help us.
"We embrace the challenge, it's what you expect at a club like Liverpool."
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