Gerrard featured in a video released by the LA Galaxy this week where he spoke about his future.
The Kop idol, 36, is set to hang up his boots at the end of the season.
Gerrard said: “Jurgen Klopp's his own man, he's got his own team of people around him that he's very happy and content with.
“There's no future decision to work with Klopp.
“I get on very well with him, we're in contact but there's no job opportunity there at the moment.
“There's nothing for me to really say on the matter. I'm a big fan of him, I hope he brings success back to Liverpool next season and I'll be supporting him from over here.
“If I had something to say I wouldn't keep supporters waiting, I'm not the type of person that would keep something under my hat and wait and delay.
“There's absolutely nothing to say on my future beyond this MLS season.
“What I can say is the phone's going, and people are enquiring 'what is the next move' and I am chewing over a lot of different things in my head but there's nothing to announce at the moment."