The Kop boss hailed the £35m signing from Arsenal as he continues to settle in to life at Anfield.
Oxlade-Chamberlain returns to the Emirates tomorrow night for the first time since quitting the Gunners to move to Merseyside.
The England midfielder has overcome a slow start to his Liverpool career to become a more influential member of Klopp’s side in recent weeks, an improvement that included his starring role in the 4-0 win over Bournemouth on Sunday.
But the Liverpool manager is expecting more – and that means goals, having netted just 20 times for the Gunners over six years.
He said: “The biggest improvement and potential is being involved in goalsoring situations. It is unbelievable but he was not asked for this too much in the past.
“If you watch Arsenal in the past their two decisive players were (Mesut) Ozil and (Alexis) Sanchez. They are involved in a lot of moments, and decisive passes. Ozil or Sanchez.