The Reds vice-captain impressed in midfield during Saturday’s 3-1 win over Athletic Bilbao after playing at left-back for most of last season.
Asked about the prospect of more new signings after being frustrated in their recent attempts to sign RB Leipzig’s Naby Keita, Klopp said: “Until August 31 we’ll run through the world with open eyes – that’s clear.
“It’s not that we decide on our own, it’s also about other clubs
“This pre-season has brought us new players. Alberto Moreno is 100% back which is really nice after a difficult year.
“Andy Robertson has shown all the skills he’s got. He’s still adapting to our kind of football but you can see what a threat he can be offensively.
“That means that Millie is free to play in midfield. Without going into the transfer market we have a new midfield player, which is nice.
“Dom Solanke has shown that he’s ready to play adult football. Ryan Kent, last season he developed unbelievably, and this pre-season has been completely different for him compared to last year.
“Without too much money or the highest transfer fees, we have additions to the squad which is good.”
Liverpool signed off their pre-season on a high as goals from Roberto Firmino, Ben Woodburn and Solanke swept Athletic Bilbao aside.
The only concern for Klopp was the slack defending which enabled Inaki Williams to equalise in the first half.
“Pre-season has been really good. We played a lot of games and we didn’t lose one – that’s a good sign,” he said.
“There were two draws, okay one of them we lost on penalties to Atletico Madrid. Performance wise most of the time it’s been good or even better.
“For half an hour today I’d say we played brilliant football. Then we lost organisation and gave them a few opportunities which changed the game a little bit. But perfection in pre-season is the biggest mistake you can make.
“We know we have to be really concentrated to be really stable. When we are stable we can play really good football.
“In the second half with a very young side we struggled a bit at the beginning but then we started playing and it was nice to see.”
Liverpool were depleted for the trip to Ireland but Klopp hopes to have Philippe Coutinho, Jordan Henderson and Daniel Sturridge back available for next Saturday’s Premier League opener at Watford.
“Everyone knows about the injury of Adam Lallana which is a big blow,” Klopp said.
“This team has had to deal with plenty of difficult situations and we will deal with this too.
“Phil had a back problem yesterday so there was no reason to take any risk. Hendo has been a bit ill and Daniel has a little muscle problem.
“We will manage it and we will rotate. From tomorrow onwards, I will be preparing for the Watford game and then the next game.”