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But there's plenty of time left in the window.
Real Madrid's forward Rodrygo and Wolves' full-back Rayan Ait Nouri have both been linked with a move to Liverpool.
In addition, Joshua Kimmich could soon be leaving Bayern Munich, with rumors suggesting he'd welcome a move to Anfield.
Keep an eye on the Liverpool.com live blog for all the latest transfer updates...
Anthony Gordon talks 'break down'
Anthony Gordon 'contact'
Van Dijk latest
KEY EVENT
Anthony Gordon talks 'break down'
Newcastle was willing to sell Anthony Gordon to Liverpool this week before talks broke down over a potential deal, according to the Daily Mail.
It's claimed that a deal proposed by Newcastle would have seen Jarell Quansah move in the opposite direction, but Liverpool decided against it.
The Reds may have proceeded with a different package, but did not make an offer after the discussions.
It's suggested that talks could be revived over the weekend.
James Findlater
PSG interest in Gordon
Further to HITC's report that Liverpool has made contact with Newcastle over Anthony Gordon, it's also claimed that PSG is interested in the England international.
Liverpool's scouts are said to have highlighted Gordon as a player whose potential could take him to the very top of the game.
They could face competition from the French champions though, with PSG chief Luis Campos said to pushed the claims of Gordon.
James Findlater
Kvaratskhelia breaks silence on future
Khvicha Kvaratskhelia has broken his silence on his future, and insisted he will make a decision after Euro 2024.
The Georgia star's agent and father have both claimed he wants to leave Napoli this summer, although the Italian club hit back in no uncertain terms by insisting he would be going nowhere.
Kvaratskhelia has now had his say, although he hasn't given anything away on his decision just yet:
I respect [new Napoli boss Antonio] Conte, he’s one of the best managers.
Now I’m focused on the game vs Spain.
James Findlater
Real Madrid enters Calafiori race
Real Madrid has entered the race for Riccardo Calafiori, according to Gazzetta dello Sport.
The italy international has starred at Euro 2024 so far, with Liverpool being linked with his signing.
They're not the only club being touted though, and the list of admirers is growing.
Real Madrid is the latest side to be linked, which could offer a hint for their plans for Leny Yoro.
James Findlater
Liverpool 'frontrunners' for Bento
Liverpool is one of the frontrunners for Brazil goalkeeper Bento, according to Globo.
Inter Milan is said to have opted against paying Athletico Paranaense’s $16m (£13m/€15m) asking price, opening the door for other sides to make a move.
Liverpool, Sporting CP and Benfica are named as the sides leading the chase for Bento's signature, who acts as Alisson's understudy with the national team.
James Findlater
Liverpool 'contacted' over Coman
Liverpool is one of a number of clubs to have been contacted about the possibility of signing Kingsley Coman, according to HITC.
With Michael Olise set to complete his move from Crystal Palace to Bayern Munich, Coman looks as though he will be dropping down the pecking order at the Allianz Arena.
Intermediaries are already said to have contacted Liverpool and others to let them know the player will be available this summer, with Bayern wanting around $63m (£50m) for his services.
KEY EVENT
Anthony Gordon 'contact'
Liverpool has made contact with Newcastle United to ask about Anthony Gordon, according to HITC.
Gordon has been linked with a surprise move to Anfield already this season following a fine season in the north-east.
The latest report claims the Reds have asked about the possibility of signing the former Everton star, although Newcastle does not want to sell.
James Findlater
Is Calafiori worth $32m transfer?
Riccardo Calafiori has been linked with a move to Liverpool this summer, and he has certainly been catching the eye at Euro 2024.
His performances for Italy have brought him to a wider audience after a fine season with Bologna, which of course means he's earning more admirers.
The question is: would he make a good signing for Liverpool?
Emmet Gates has taken a closer look here.
James Findlater
Luis Diaz latest
A move to Barcelona could potentially stall for Luis Diaz, with the club's new boss Hansi Flick reportedly preferring Nico Williams.
Sport claims that while club chiefs prefer Diaz, Flick is more keen on Williams, himself linked with Liverpool.
Diaz was on the scoresheet for Colombia in their 3-0 win over Costa Rica at Copa America.
Tom Blow
Will Salah leave Liverpool this summer?
Mohamed Salah is not expected to leave Liverpool this summer, but it's too early to say for sure.
Salah, who has just celebrated his 32nd birthday, has just a year left on his contract and was a target for the Saudi Pro League last summer.
For more news relating to Newcastle United, visit our sister site NUFC Latest Live.