The duo have returned to training at Melwood following injury, but are unlikely to come into contention for Monday’s Premier League encounter with Swansea City at the Liberty Stadium.
Klopp told Liverpoolfc.com: “Hendo will today have a clearing session. He was part of training yesterday morning and today is clearing, then he should be OK from tomorrow onwards.
“It is close, but maybe close and not enough time for Swansea – but [after that] Hendo is back and that’s good news.
“Alberto is back in training a few days longer and we have to see. Because it is Alberto, he trains all the time and feels it still a little bit – in one or two movements you can see.
“We will not put any rush on him, but he will be back for sure after Swansea as well – or even maybe Swansea, I’m not sure.”
Meanwhile, Klopp confirmed Nathaniel Clyne continues to make good progress in his rehabilitation from the back problem that has kept him out of all of 2017-18 so far.
He added: “Clyney is doing well but still a little way to go until he is back in completely normal training. He is doing well, really good.”