Liverpool boss Jurgen Klopp is reportedly pushing for the club to hand Thiago a contract extension.
The 32-year-old's current deal at Anfield is due to expire next June, and there has been a host of speculation surrounding his future in recent months.
Thiago arrived at Liverpool from Bayern Munich in the summer of 2020, and he has represented the Reds on 97 occasions in all competitions, scoring three goals and registering six assists.
The Spain international was restricted to just 18 Premier League appearances last term, though, due to a number of fitness problems.
This season, Thiago is yet to feature, as he works his way back from a hip problem that he suffered in April, and he will again miss out against Tottenham Hotspur on Saturday.
According to 90min, there is a divide in the Liverpool camp when it comes to the best course of action for the experienced midfielder.
The report claims that Klopp is desperate for Thiago to be handed an extension, but there are senior figures at the club who would be prepared to let him leave on a free transfer next year.
Thiago is currently one of the highest earners at Anfield, and there is a possibility that he could be placed on the market ahead of the January transfer window.
Many clubs in Turkey and Saudi Arabia are said to be keeping a close eye on the situation with a view to potentially signing him at the start of 2024.
Liverpool assistant manager Pep Lijnders said last week that the club are 'missing' the midfielder's "quality".
"He is in a good way, the healing process is going well so that's the most important [thing] at this moment," he told reporters.
"We miss Thiago, his quality. Alexis [Mac Allister] shows a lot of similar control in the middle, makes the ball arrive in the right spaces to the right players.
"We want him back in training, he is still not back in training. He's healing and is individual on the pitch, simple but effective. Time will tell how that goes."
Liverpool brought in four new midfielders over the summer, with Dominik Szoboszlai, Wataru Endo and Ryan Gravenberch following Mac Allister to the club.
