Gerrard took over at Rangers in June and has suffered just one loss in 13 games at the helm of the Scottish giants, helping them qualify for the Europa League group stage.
Klopp praised the Liverpool great and confirmed he was in contact with the 38-year-old, but not to offer advice.
"Rangers were brilliant in Europe — Gerrard is putting a good team together," Klopp was 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."
Gerrard's first loss in charge of Rangers came on Sunday, beaten 1-0 by rivals Celtic.
Despite that defeat, Klopp said Gerrard's men – who are seventh in the Scottish Premiership – had closed the gap to the champions.
"He's made a brilliant start at Ibrox — then he lost against Celtic. Wow, what a surprise," he said.
"Celtic are the top team in the league, but it's not like they were 50 or 60 per cent 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."