Gerrard has stated he doesn't want to replace Klopp at the stage in his managerial career.
But Reds fan Solbakken told TV2: "This gives scars all the way into next season. On a day when Steven Gerrard has become Scottish champions with Rangers, Klopp suddenly has a pressure on him that was totally unthinkable a few months ago. If they open a little badly next season, and Gerrard stands and trips a little in Glasgow, you can quickly shake hands, because that's how the game is here.
"Maybe he does not want to train Rangers that much anymore and I think many clubs in England would like him.
"I still believe that Klopp is the best to turn it around, but this industry works in such a way that whether you are called Klopp or something else, a bad start next season will put him under a completely different pressure."