Klopp, who has succeeded Brendan Rodgers as the Reds manager, said in a press conference on Friday morning that he aims to win the league title inside the next four years.
"If we sit here in four years, I think we'll have won one title -- I'm pretty sure,” ESPN quotes the German as saying. “If not, the next one may be in Switzerland.”
Former United goalkeeper Schmeichel has mocked Klopp on Twitter, suggesting that he has made his first mistake by promising to win the Premier League title.
Jurgen Klopp: "If I sit here in four years, I am pretty confident we will have one title." #LFC— Ben Smith (@BenSmithBBC) October 9, 2015
Never ever seen a better press conference from a new manager! The energy, how he speaks, everything! Give this guy time! What a man! @LFC— John Arne Riise (@JARiiseOfficial) October 9, 2015
Great start for Klopp in England. Refreshing to see the humility he showed. Doesnt take himself too serious unlike some others.— Didi Hamann (@DietmarHamann) October 9, 2015
Liverpool are 10th in the Premier League table at the moment with 12 points from eight matches, just three points behind fourth-place Crystal Palace.
The Reds are very much in the running for a top-four finish in the Premier League this season, and fans will hope that Klopp can galvanise the team.
The Merseyside outfit will take on Tottenham Hotspur away from home at White Hart Lane in the league after the international break.