The Reds boss penned a contract extension that runs until 2024 in December, with the club appearing destined to lift the Premier League trophy at the end of this season.
But McAteer told beIN Sports: "He has a team around him, Melwood is locked down, you can't get into it. It's the hub.
"No [I wouldn't be surprised if he walks away]. It wouldn't surprise me, it wouldn't surprise me at all. I just think there's burnout.
"The passion he puts into it, the effort he puts into it, it's all the time.
"I've been on tour with them before, he can't move. He can't go out the hotel, he's meeting potential partners, he's going to dinners, they're putting things on, it's constant.
"The partnership side of the club, when they come in and they want something, they want to get their name out there, who do they put on the front?
"Out of all the players, first it's [Mohamed] Salah, then it's Klopp. Before [Roberto] Firmino, before [Virgil] van Dijk, before [Sadio] Mane, it's Klopp."