Reds midfield legend Gerrard has lost just one of his opening 13 matches in charge of the Gers since officially taking over in June.
The 38-year-old has guided the Glasgow club back into the Europa League for the first time since 2011, and is now tasked with ending Celtic's dominance at the Scottish Premiership summit.
Klopp says that Gerrard can be pleased with his first few months in the dugout, despite losing 1-0 to Celtic in his most recent match.
"Rangers were brilliant in Europe - Gerrard is putting a good team together," he is quoted as saying by The Mirror. "When I started out as a manager I didn't ask for advice because I didn't know who to ask. Steven doesn't ask because he doesn't have to.
"We are in contact, but not for advice. He's made a brilliant start at Ibrox - then he lost against Celtic. Wow, what a surprise!
"Celtic are the top team in the league, but it's not like they were 50 or 60% better than Rangers like they have been in the last few years. Rangers are getting closer and that's the only way to get them one day. That's Steven's job, but so far it's more than good."
Rangers return to action next weekend with a home league match against Dundee.