Liverpool, who are 22 points clear of Manchester City, are on the cusp of a first top-flight title since 1990 and need just two more wins to guarantee lifting the trophy.
Boss Klopp said he feels it is impossible for one club to enjoy the sort of success United did under the legendary Alex Ferguson, who won 13 Premier League titles during his 26-year stint.
Former United captain Rooney – a long-time foe of Liverpool due to his association with Everton and the Red Devils – disagrees, though, and tipped the Anfield club to win the league at least five times in the next decade on the proviso Klopp remains at the helm.
"Liverpool's squad is young and all the key players are tied down on long contracts. They have huge potential to win more trophies," Rooney wrote in his column for The Times.
"Klopp says it's impossible for any club to dominate like United once did but he is wrong.
"There's a simple way for Liverpool: let Klopp go on and on.
"United dominated because Fergie stayed so long. I think if Klopp, who is only 53, stayed at Anfield for the next 10 years Liverpool would win at least five Premier League titles.
"He could keep building great sides because, as I mentioned, players join clubs to work with managers as good as him.
"On the flip-side, players stay at clubs because of managers, too. And if Klopp left it would be no surprise to see the likes of Mohamed Salah, Sadio Mane and Roberto Firmino also deciding to move on.
"If I were one of Liverpool's owners, I would be doing everything in my power to tie him down for many years."
Rooney won the Premier League five times playing for Ferguson at Old Trafford, while he also became a Champions League winner under the Scot.
Liverpool's first game back since the suspension of the top flight due to the coronavirus pandemic is Sunday's Merseyside derby at Everton.