Relevo says Liverpool have no plans to offer a new contract extension.
Their decision is mainly based on Thiago's injury problems, but also that he is among the best paid players in the squad.
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Thiago earns 10m-a-year and the midfielder has no plans to retire.
However, Thiago wants to get fully healthy before making a decision on his next destination.
The most likely option is that Thiago is looking for a last big contract in Saudi Arabia or Qatar.