On Tuesday, the Reds reportedly saw a third offer believed to be worth in the region of £46m rejected by Southampton.
The Championship side are believed to be holding out for £50m for the 19-year-old despite their relegation last season.
Summer signing Mac Allister was deployed in a deeper role as Klopp’s side beat Darmstadt in their final pre-season game before the Premier League kicks off this weekend.
Liverpool’s midfield attracted a lot of the criticism during what was a difficult campaign last time out and has since been rebuilt.
The Argentina international and Dominik Szoboszlai have arrived, while all of Jordan Henderson, Fabinho, Naby Keita, James Milner and Alex Oxlade-Chamberlain have departed.
While Mac Allister and Szoboszlai offer something new, neither are recognised defensive midfielders.
Speaking after the win at Preston North End’s Deepdale, Klopp said: “We have to try it and test a couple of different things. Yes, in a compact formation, Alexis can play there, definitely. If he’s there alone, should he play there?
“No. But now he showed just how good a footballer he is and how good he understands the game because he played here now [for] the first time for us at least and he did really well.”