Gerrard?s comments are bound to fuel speculation that the highly popular Liverpudlian could return to play for the club he first represented 18 years ago and for whom he made over 500 appearances.
Klopp has previously indicated that such a possibility would not be realistic for the veteran although, following Saturday's 2-1 victory over West Bromwich Albion, the Liverpool manager declined to explain exactly what role could await a player who also made 114 England appearances in one of the most successful careers of the modern football era.
"Stevie Gerrard is always so welcome at Liverpool FC, you can?t imagine how welcome," said Klopp after his team's win at Anfield.
"So there is absolutely no problem. But anything we have, or will, speak about, stays (between us). That's how I know Stevie, that?s how I am.
"But nobody should be worried that there is no space for Steven Gerrard. Everything will be fine, 100 percent."
While it is understood Gerrard is keen to pursue a coaching career, it is believed that such a position will not be available under Klopp and that an ambassadorial role is the one likely to be on offer now to the Anfield great.
Gerrard, in an Instagram post, said: "Living in Los Angeles and playing for the great Galaxy supporters has been a privilege. You have made this place feel like home to me. This city and this club will always hold a special place in my heart. Thank you."
Meanwhile, beaten West Brom manager Tony Pulis said Klopp could improve on the efforts of his predecessor Brendan Rodgers, who was narrowly beaten to the title in 2014, and end Liverpool's 27-year wait to be crowned champions of England.
"They?re a good side," said Pulis. "Their front five are as good as anything in the league.
"They?ve got a free run at it this year (season). They're not in Europe which is draining, irrespective of what people say, I?ve been there myself. So they have a free run.
"The last time they came close, with Brendan, they had a free run as well and they have a free run at it this year," he added.
Klopp saw his team edge closer to the top of the table with first-half goals against West Brom from Sadio Mane and Philippe Coutinho, only for a late consolation effort from Gareth McAuley to deny his team the two clear goals they needed to go above leaders Arsenal.
"Who wants to be top in October?" said Klopp. "Okay, it was a little bit of a joke but we have 20 points and it was not possible to have more tonight, so that?s okay.
"Maybe not having clean sheets is just part of our game, I don't know. It's not a big problem. Defending is, first of all, about not letting them create a lot of chances and I can?t remember a lot of chances the last few games.
?In dreamland, then you always win 4 or 5-0 and then the crowd can go home a little bit earlier to do something more serious but I actually think this game created one of the best chances we have had here because it was exciting until the end.
"It?s really difficult to be satisfied with any football game and, at 2-1, it keeps you more awake than at 4-0. That's just how it is. Maybe in this moment we?re not experienced enough in a situation like this.?