The Daily Star says they will look to land Markovic if their move to sign Adam Lallana fails.
The Reds have been told to pay £30m for the Southampton star.
They have already had two bids - of £20m and £25m - turned down.
Kop chiefs are still hopeful of getting the Saints skipper but are making back-up plans in case the move fails.
Markovic had been linked with a move to Chelsea but is now understood to be keen to move to Anfield.
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