The 19-year-old was officially snapped up by the Reds from Premier League rivals Chelsea earlier this week, fresh on the back of playing a starring role in England's World Cup success at Under-20s level.
Solanke was the only debutant on show in Liverpool's opening pre-season fixture, a 4-0 win over Tranmere Rovers on Wednesday night, due to immigration red tape blocking Mohamed Salah's first inclusion.
Klopp is happy with what he saw from the youngster at Prenton Park, insisting that there is a chance he will be fast-tracked into the first team next term if he does enough to impress.
"He decides that himself. Obviously he is a young lad and it is a long-term project. I have all the time in the world," he told reporters. "If he brings a little bit 'rush' with his development then everything is good.
"I saw a few wonderful signs tonight and I think everyone in England watched the Under-20 championship - that was fantastic football. He is a really skilled boy. He has to improve of course but a lot of things are already really good - first touch, movement.
"It is about him and the situation but I will not avoid his development. In the moment when he is strong enough he is there. He will train with us, of course, as often as it makes sense and often as possible and then we will see."