The south-coast club have set a price tag of around £40m for the 21-year-old left-back, who has three years left on his contract.
Kerkez is understood to be keen on the move and personal terms are not expected to be a problem.
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The Hungary international has been one of Bournemouth’s stand-out players this season and Liverpool have been keen on him for some time.
Liverpool’s sporting director Richard Hughes originally signed him for the Cherries from AZ Alkmaar in 2023.
Wirtz only wants Liverpool move with talks ongoing
Meanwhile, Florian Wirtz only wants to join Liverpool with talks over a potential club-record deal continuing with Bayer Leverkusen.
Leverkusen want a deal that values the player at £120m. Wirtz is with the Germany squad preparing for their Nations League semi-final against Portugal in Munich.
Bayern Munich and Manchester City are also trying to sign the 22-year-old, who was among the Bundesliga’s most impressive performers last season.
Wirtz, who has spent his entire senior career at Leverkusen, scored 10 goals and registered 12 assists in 25 starts as his side finished runners-up to Bayern Munich, a year on from winning a league and cup double.
Carra: Liverpool need a new left-back
Sky Sports’ Jamie Carragher believes Liverpool need to sign a new left-back before targeting a centre forward.
“Throughout the season, I was still saying that Liverpool still need five or six players,” said Carragher on The Overlap.
“I think the left-back comes in and plays straight away, Frimpong will fight with Conor Bradley, Wirtz will play when he comes to the club. But I still think we need a centre forward. I think Liverpool will look to get their business done pretty early.
“Liverpool need a left-back, Andy Robertson needs help on that side and Kostas Tsimikas will be moved on. I’ve always felt that attacking midfield and left-back are the two areas that have jumped out to me in the last 12 to 18 months.
“Whether Wirtz comes in and plays in Szoboszlai’s role or plays from the left, I don’t know. But the next one is centre forward and I wouldn’t be surprised if once Liverpool get these three [Frimpong, Wirtz, and the left-back] done, the next one will be a centre forward.
“As the window goes on, Liverpool will just see who they can sell and what they can do – they might bring in another midfield player or a centre-back to back up, but they’ll just assess what the situation is.”
Follow the transfer window on Sky Sports
The first of two summer transfer windows is upon us – and there is no better place than Sky Sports to get all the latest transfer news and rumours.
Use the Sky Sports app and website for all your updates in our dedicated Transfer Centre and Premier League club blogs, plus live Q&As with our reporters throughout the summer.
The Transfer Show returns to Sky Sports News from Sunday June 1 for the start of the pre-Club World Cup window and will then be on every weeknight at 5pm and 7pm until the deadline on Tuesday June 10.
The summer transfer window will open again on Monday June 16 until Monday September 1 – with the deadline brought forward to 7pm this year
