TalkSPORT reports the Reds do want to sign the Spanish midfielder in this transfer window.
But they do not want to pay over the odds. And as a result, they are prepared to let the saga run until the final week of the transfer window.
The Reds believe Bayern Munich will be more willing to negotiate a lower fee when they realise no one else has come in for the player.
Thiago wants to go to Liverpool, and may even sign as a free agent next summer if the move does not materialize this time around.