Inter Milan are prepared to pay £30m for Curtis Jones, though Liverpool are holding out for more, the latest report has claimed.
The Reds are back in pre-season action on Sunday, when they take on Premier League opponents Leeds United in Chicago.
Andoni Iraola will likely name a stronger lineup for that match than in his first two friendlies in charge of the club, and it will be fascinating to see if Jones is part of the XI.
The 25-year-old has just a year left on his contract, and he was subject of a failed bid from Inter Milan earlier in the transfer window worth just over £20m, significantly short of the Merseysiders' reported demands of £35m.
A new story from the Daily Mail claims that Inter are ready to bid £30m for the boyhood Reds fan, though Liverpool are likely to hold out for more.
Curtis Jones assessed: Should the Reds sell midfielder?
Jones has been a controversial figure amongst Reds fans for some time, with his supporters arguing that he has developed significantly, while his detractors claim that he has failed to deliver on the promise he showcased earlier in his career.
The 25-year-old is statistically one of the best players in the Premier League when it comes to ball retention given his pass accuracy of 91.6% was the second best amongst midfielders in the division last term.
Jones has been frequently criticised by pundits for supposedly playing too safely, with the likes of Jamie Carragher claiming that he holds onto the ball for too long.
While he can at times be guilty of such accusations, he has often demonstrated an ability to play forward into the final third over the past two seasons.
However, with a year left on his contract, Liverpool cannot afford to keep him at the club if he is determined to play a bigger role, so an exit may be in the best interests of all parties.
Curtis Jones replacement: Who should Liverpool sign?
Selling Jones would free up a space in the squad for another midfielder, and perhaps the Reds could reignite their interest in someone such as Adam Wharton.
The Crystal Palace star is one of the best creative players in England from deeper areas, and he may help unlock the full potential of Florian Wirtz and Alexander Isak.
If the Reds want a more combative presence in the middle of the pitch, they could look to sign Monaco midfielder Lamine Camara, whose ability to win possession would suit Iraola's high-pressing system.