The Reds claimed their second trophy of 2021-22 when defeating Chelsea on penalties in the FA Cup final.
Liverpool also beat the Stamford Bridge outfit on spot-kicks to claim the Carabao Cup in February.
Klopp’s troops also have the small matter of the Champions League final against Real Madrid in Paris at the end of the month.
What’s more, the Reds sit three points behind Manchester City in the Premier League with two games to play - and still have a chance of claiming the title.
However, given the arduous game against Chelsea - coupled with the high possibility of City winning against West Ham today - Klopp admits it’s unlikely Liverpool can catch Pep Guardiola’s side and potentially create history.
What’s been said
Speaking after the FA Cup triumph, Klopp said: “I’ve said before the quadruple thing is absolutely outstanding we can talk about it, it’s crazy.
“We sit here, it’s already 21.20 and we play on Tuesday night against Southampton.
“I think we will have to make a few changes. We will go there, Southampton’s last home game of the season for them and don’t want to lose the last home game. It will be incredibly tough.
“The quadruple is on, if you want, but off as well because of the situation.
“But that’s not important in the moment. We won both domestic cups and that’s really special.
“Trent Alexander-Arnold is the youngest player in the Premier League who won all six major trophies at 23. It’s madness. So many special stories.
“After the game, I said to Thiago, if I knew what a player you are, I would have signed you four years earlier! He said: 'You taught me running'.
"He could already play football really well, but he learnt running at Liverpool, that’s fine.
“So many special stories. Jordan Henderson, it’s really good. James Milner having such an impact on a football team.”