The 25-year-old forward, whose contract with Juventus expires at the end of the current season, is keen to test himself in England and is prioritising a move there if he leaves Turin.
His reported salary demands of around 150,000 pounds are seen as affordable only by Premier League clubs at present, ruling out many continental contenders.
Newcastle United have emerged as the likeliest destination, particularly with Alexander Isak pushing for a blockbuster move to Liverpool.
Should the Swedish striker depart, Newcastle would need a marquee replacement and see Vlahovic as a natural fit.
The Magpies are also seeking reinforcements up front after Callum Wilson's exit, with Brentford's Yoane Wissa and Wolves' Jorgen Strand Larsen also on their shortlist.
Liverpool's interest is closely tied to Isak's future. Should they succeed in luring him to Anfield, Vlahovic would become a key part of Newcastle's succession plan.
Meanwhile, AC Milan are monitoring the situation but would only pursue the Serbian if he slashed his salary demands by more than 30 per cent to around 6m euros annually - a cut he is unwilling to accept.
Anthony Gordon has issued a public apology to his Newcastle teammates, fans, and Liverpool captain Virgil van Dijk following his red card in the dramatic 3-2 loss to the Reds at St James' Park on Monday.
Liverpool's pursuit of Crystal Palace defender Marc Guehi has gained momentum as the Eagles have reportedly tabled a daring offer for Manchester City's Manuel Akanji, potentially clearing the path for Guehi's departure.
Sky Sports pundit Jamie Carragher tore into Liverpool's Mohamed Salah and Ibrahima Konate after the Reds scraped a thrilling 3-2 victory over Newcastle United on Monday, at St James' Park.
In a pulsating Premier League clash at St James' Park on Monday, 16-year-old Rio Ngumoha emerged as Liverpool's hero, scoring a dramatic 100th-minute winner to secure a 3-2 victory over a resilient 10-man Newcastle United.
