Reds boss Brendan Rodgers wants to add more goals to his ranks in the January window and Sturridge is known to be high on his wanted list if a deal can be agreed.
However that looks unlikely at this stage as reports claim the Reds are unwilling to meet player's demands of £80,000 a week and will now look elsewhere.
Rodgers could now turn to his former club to try and land Michu, but any approach will not go down well with the hierarchy at the Liberty Stadium following the departure of Joe Allen to Anfield.
Swansea face a battle to keep Michu, who bagged another two goals against Norwich at the weekend to take his tally for the season to 13, but it will take big money to prise him away.
Last week Michael Laudrup slapped a £30million price tag on his head and although that seems a bit excessive, he will cost more than Allen and that could scare Liverpool off.