A life-long Reds fan who became the youngest player in Everton history when he made his senior debut in 2008, Baxter has excelled with Oldham since leaving Goodison Park in search of regular first-team football.
The last of his 11 goals in 27 appearances to date came as Latics stunned Nottingham Forest 3-2 in round three, and the 20-year-old was enjoying a well-earned lazy Sunday when the fourth-round draw took place a day later.
"I was lying in bed, just watching the draw itself," he said. "I was actually dreaming of Liverpool to be honest and it came out.
"It was mad, I got loads of texts from friends and family so it was a really good day.
"It's going to be great for me, being a Liverpool fan - it's going to be massive."
Life as a professional since his formative years has not dulled the enthusiastic fan in Baxter.
"I try to get to every (Liverpool) game I can when I'm not in training or not playing. I've followed them all around the world as a young kid growing up," he said.
"Steven Gerrard is my idol. He has been for many years and he's someone I look up to. I'd love to be half the player he is.
"But on Sunday I wouldn't really ask for shirts and stuff like that. I wouldn't go on the pitch if we lost and ask for shirts. If I was to do it, it would be behind the scenes."