The former Borussia Dortmund manager was named as Rodgers’s successor in October following the Merseyside derby at Goodison Park.
Rodgers led Liverpool to second place in the Premier League table in 2014 but the Reds finished seventh in the Northern Irishman’s third season in charge at Anfield.
Klopp’s side are in sixth place following Sunday’s 2-1 victory at Crystal Palace but six points behind fourth-placed Manchester City in the race to secure a place in next season’s Champions League competiton.
Former Liverpool boss Rodgers believes Klopp will be given the time by the club’s owners to turn the Merseyside outfit into Premier League champions.
“They have a very good manager in Jurgen Klopp,” Klopp told Belfast Telegraph.
“It is going to take time to bed in his methods and how he wants to work. He has some very good players there.
“The expectancy of course is to win the league, we went very close in my time and obviously Jurgen will go in and feel that he can improve on that and that’s why the owners made the change.
“They felt they wanted to improve and to improve on runners-up would be to win the league but it is going to take time.
“I’m sure the owners will give him that time.”
Liverpool face Manchester United in the first leg of their Europa League last-16 tie on Thursday night.
The Reds haven’t beaten their bitter rivals since a 3-0 at Old Trafford in 2014.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news