The fixture is set to be arranged for the period following next weekend's Premier League meeting with Southampton at Anfield, when Klopp had planned to give his players a full week off.
And the 52-year-old has revealed he still plans to hand his regular first-team players a much-needed rest, while also taking time away from the dugout himself.
"Our situation is the following: we've known for a couple of weeks, in fact we've known longer, that it would be like this," he said.
"In April 2019 we got a letter from the Premier League, I think, where they asked us to respect the winter break and not to organise international friendlies or competitive games. We respect that.
"So I said to the boys already two weeks ago that we will have a winter break which means we will not be there. It will be the kids who play that game.
"You cannot deal with us like nobody cares about it. I know that it's not very popular but that's the way I see it.
"The Premier League asked us to respect the winter break. That's what we do. If the FA doesn't respect that, then we cannot change it. We will not be there.
"Does that mean I won't be there? Yes."