The Spain international is now in the final year of his contract with the Anfield giants and has been tipped to leave this summer as part of their midfield overhaul.
Jordan Henderson and Fabinho have already made lucrative moves to the Saudi Pro League this summer, while Naby Keita, Alex Oxlade-Chamberlain, James Milner and Leighton Clarkson have also departed for pastures new.
With Dominik Szoboszlai and Alexis Mac Allister arriving to compete with Stefan Bajcetic, Curtis Jones and Harvey Elliott for midfield starts, minutes may be even harder for Thiago to come by next term.
The former Bayern Munich man was allegedly the subject of a €12m (£10.4m) offer from Al Ahli earlier this week, but according to Fabrizio Romano, he is not in active talks with the Middle Eastern side.
Romano adds that Thiago has already rejected several approaches from Saudi Arabian teams this summer, as the 32-year-old is focused on helping Liverpool achieve their goals for the 2023-24 season.
Jurgen Klopp is believed to be planning for the upcoming campaign with Thiago in the fold, but Liverpool are unlikely to sanction a contract extension for the midfielder beyond next summer.
As a result, Thiago will likely be departing the club on a free transfer at the end of the current season, bringing an end to an injury-hit four-year stay with the Merseyside giants.
The Spaniard arrived in 2020 amid concerns about how he would fit in to Klopp's high-intensity system, but he has proven to be a valuable member of the Reds' squad when fully fit.
Thiago has amassed three goals and six assists in 97 games under Klopp's tutelage, winning the FA Cup, EFL Cup and Community Shield during his second campaign.
However, the ex-Barcelona man has sat out a further 66 games due to a combination of injury and illness woes and came up with just one assist from 28 appearances in the 2022-23 season.
Thiago only started 14 Premier League games last term due to a troublesome hip problem, and he has not taken to the field in pre-season while he recovers from his recent operation.
Thiago is being put through his paces at Kirkby, but it is still unclear whether the midfielder will be passed fit for Sunday's Premier League opener against Chelsea at Stamford Bridge.
Given their plethora of midfield exits already this summer, Liverpool are working on a deal for Southampton's Romeo Lavia and are understood to have made contact with Brighton & Hove Albion's Moises Caicedo, but no bid has been tabled yet.