Concern has been raised as Robertson has just undergone surgery on a hand infected after an insect bite.
Youngsters Adam Lewis and Yasser Larouci have each played 45-minute halves in the club’s two pre-season friendlies but Klopp may yet decide a new external recruit is what is required.
“We will see. It’s not a yes, not a no,” said Klopp after a 3-1 victory over Bradford.
“I have said already we have to think about everything and at the end maybe we do nothing.
“I can imagine we have a look at all the things around us. Of course, we lost a left-back [in Moreno] but today we saw two pretty young ones, and James [Milner] played it. We will see.”
Klopp has also deployed Adam Lallana as the deep-lying midfielder in both friendlies so far, and while he has not decided whether that could be a long-term role for him, he is more concerned with ensuring the player remains fit after 18 months of niggles.
“Adam is the kind of player he can play that and he enjoys this ‘Jorginho’ role—I hope Maurizio Sarri doesn’t see the games or he will make an offer,” added the manager.
“It is about getting Adam rhythm, bringing him in early and doing things he is naturally good at—small spaces, passing the ball, and then from time-to-time offering the runs in behind as well and together with Milly that is possible. For us, it is another option.
“He needs a bit of luck, as we all do in life. We have to come through without injuries, that would be cool, and then we have a couple of new players, I would say, this season.”
The match at Valley Parade—watched by a crowd of 24,343, the highest since the stadium reopened in 1986—raised money for the Darby Rimmer MND Foundation, a charity set up by former Liverpool and Bradford player Stephen Darby and his friend Chris Rimmer after both were diagnosed with motor neurone disease.
At half-time Milner also presented a cheque for £30,000 from his own foundation to Darby, with the midfielder’s charity donating a further £10,000 for motor neurone disease research.
Earlier, Milner’s strike had deflected in off Bradford’s James Vaughan before the Liverpool midfielder converted a penalty, with Eoin Doyle scoring with a late spot-kick for the hosts.