The Reds face Oldham in the FA Cup third round with Anton, who signed with the Latics in the summer, in line to play after featuring 13 times for the League One side so far this term.
But father Brendan has no intention of going easy on his son, with Athletic having beaten Liverpool 3-2 in the fourth round of the competition last season.
"In all seriousness, that's the job - but it is also a situation that I will want my players to pay attention to, because the footballing gods sometimes come into it as well," Rodgers senior told several national newspapers.
"With the footballing gods, he could end up getting a goal.
"But not only that, I have to get the team to keep an eye on him because he's a good player.
"He's got quality, he has a great view of the game and he's a real footballer. So I can't skip over it because it's Anton. This is business."