But midfield is not the only area Liverpool want to strengthen, with Klopp also having been keen to bring in a new winger to provide cover and genuine competition for his first-choice front three.
The Merseysiders have been heavily linked with Watford’s Ismaila Sarr, who is likely to cost in excess of £40m, but may instead opt for a cheaper alternative.
According to Spanish newspaper Sport, Liverpool have made their first official contact with Barcelona over a move for out-of-favour winger Dembele, who arrived at Camp Nou for an initial £96.8m fee three years ago.
He has struggled to live up to that price tag but Klopp remains a big fan, with Liverpool enquiring about the possibility of taking Dembele on loan.
The champions would pay a loan fee and take on the entirety of his salary, which is believed to be over £200,000-a-week – which would make him one of Liverpool’s highest earners.
Although Klopp has largely been coy on Liverpool’s potential transfer business this summer, he intimated that more deals could happen before the deadline.
Speaking at his pre-match press conference before facing Chelsea, the German coach said: ‘The window itself leaves the window open, because it’s open until October 6. And longer, in one way, I think. So that’s normal.
‘But that was always the same. I cannot promise that we will do something and I wouldn’t. But I cannot say it’s 100% sure that we don’t do anything. So it’s just the situation.
‘It’s a developing situation, so everything could happen until October 6. A player comes to me and asks me, “Boss I want to go” – I don’t expect that but it can happen – then we have to react and all these kinds of things can happen.’