The Reds coach has been unable to call upon Clyne and Lallana for the duration of the season so far due to respective back and thigh problems.
There is still no specific return date for the pair, but during a pre-match press conference on Monday, Klopp delivered an update on the duo's fitness.
"Clyney had the third or fourth run outside yesterday, not the highest intensity but a big step and he coped well so far with this," the former Borussia Dortmund boss told reporters.
"Adam is close to going outside and running. For the next step, I'll give you another update in the next press conference."
Liverpool are preparing for Tuesday night's EFL Cup clash away to Leicester City.