Wilder and United are one of the biggest opposers of the ongoing push to revert to five substitutes, while Klopp is one of its biggest backers.
In the week, Wilder descriped Klopp as a “world-class manager and a world-class politician” who only cares about Liverpool, rather than Sheffield United or any other Premier League club.
That quote was actually in relation to getting fans back in stadia – Liverpool is a tier two city, so can have some supporters at home games, but United in tier three cannot.
“He’s a world-class manager and a world-class politician, who cares about Liverpool,” Wilder said. “That’s all he cares about.
“He was never going to say what about Sheffield United getting their fans back in or Newcastle or Man. City or Man. United or anybody else. He’s a world-class politician.
"Cards on the table… he is going to look after his own club. I’ve got incredible respect for these top managers because they produce top results and win things."
But Klopp, unprompted, raised the issue in his post-match interview following his side’s 1-1 draw with Brighton this afternoon.
"They had injuries as well, but ask Chris Wilder how we can avoid that,” Klopp said.
"Chris Wilder says I am selfish. I think all the things he says are selfish.
"I was in a similar situation as he is when I worked at Mainz - all about staying in the league.
“But they now have three subs, and one point, if I’m right, so there’s no advantage or disadvantage.
"If I had five subs today, I bring on Kostas for Robbo, to save Robbo. It’s not about tactics. It's about saving players."