Liverpool have made an offer for Croatia defender Domagoj Vida, according to the player's agent.
However, according to the Daily Express, Jurgen Klopp will need to beat off stiff competition from city rivals Everton in order to land the Besiktas centre back.
It is understood that the Istanbul club will want at least £22m for the player this summer.
Elsewhere, West Bromwich Albion are the latest club to register interest in the Liverpool winger Sheyi Ojo as they bid to make an immediate return to the Premier League next season, says the Guardian.
The England U21 international spent last season on loan at promoted Championship side Fulham.
Meanwhile, Jose Mourinho believes Liverpool's summer spending means they face immense pressure to win the Premier League, with the Manchester United boss labelling Jurgen Klopp's change in transfer policy as "funny".
Klopp has been forced to defend Liverpool's expenditure on players, which topped £170m after signing goalkeeper Alisson last week, two years after the Liverpool boss was critical of United's £90m move for Paul Pogba.
"I'm happy to smile [about Klopp's previous comments] and to see that, you know, you can change your opinion and change as a person, it's funny," said the United boss.
"That's okay, but maybe this season finally you demand that they win. I think you have to be fair and now you have to demand [they win the league]."