They could delay making a move for Thiago in a risky attempt to land him on a free transfer.
The 29-year-old midfielder is out of contract next June but Bayern Munich are willing to offload him this summer in a cut-price £27million deal.
While Liverpool are keen on signing the midfielder, Sky Sports' Dharmesh Sheth claims there is “no way" the Merseyside club will part company with that sort of cash for a player available for nothing in less than a years time.
Thiago is able to sign a pre-contract agreement from as early as January - just three months after the transfer window shuts.
Even then if Liverpool wanted to sign Thiago before next summer his price would have fallen further, but they are not said to have a burning need to add the player to their squad.