The Premier League's joint leaders are seeking a third consecutive victory from the start of the season -- a feat they have only achieved four times since 1990.
"If you're 32 in any company in the world they tell you wait a few years until you can get a real job but in football it sounds like they're close to retirement," said Klopp.
"But our players could play until 38 and I'm sure he's one of them if he can keep free of injuries.
"I didn't work with Milner (when he was younger) but he is always good since I worked with him. His desire to keep free of injuries is exceptional."
Milner, who is teetotal, has been playing top-flight football for half his life, making his debut as a 16-year-old for Leeds United and going on to make approaching 500 league appearances and winning 61 caps for England before announcing his international retirement.
Klopp now has a wealth of options in midfield, with new signing Naby Keita impressing in his opening games and Jordan Henderson yet to start.
The German knows he has to rein in rising expectations this season when Liverpool are tipped to provide Manchester City with their main title threat.
Yet he warned they will have to be at their best against Brighton, who will be boosted by last week's 3-2 win over Manchester United.
"They are a really good team and I respect a lot what Chris (Hughton) is doing there, not just the Man United game.
"They're very good, organised and on point. United had chances for a much better result but we are warned. We have to be 100 percent."
Klopp also paid tribute to Sadio Mane, who is outscoring team mate Mohamed Salah this season with three goals from his opening two games.
"He plays his third season here. He has constantly improved. We really knew we would get a good player," he said.
"Did we know exactly how good? I wouldn't say so. He's stepped it up. He’s a very nice person. That's it. All the others benefit from good players around but we can still improve and so can Sadio but his consistency is quite impressive."
Klopp also said he expected centre half Dejan Lovren to remain out until after next month's international break, adding that there were no new developments on keeper Loris Karius's expected move to Besiktas.
(Reporting by Neil Robinson; Editing by Toby Davis)
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