Gerrard announced his retirement as a player on Thursday after his contract with the Los Angeles Galaxy expired.
The 36-year-old former England and Reds captain has already turned down the chance to manage League One MK Dons but is looking at moving into coaching.
There have been suggestions Gerrard could get a role somewhere at Liverpool - Klopp virtually guaranteed it - and possibly with the youth teams
However it seems highly unlikely he will be invited into the German's well-established inner sanctum with the first team.
"This is not the room to speak about it. There is nothing to talk about and I am absolutely the wrong person to talk about it," said Klopp in a press conference.
"When something is announced then we will talk. It is clear that one day in the future there will be something to announce, that is pretty sure too, but until then there is nothing to say.
"The door is always open for him. If he wants to make a different career to his former career then we want to help him.
"There is nothing else to say - but maybe that is already too much."
Source: PA