The Colombian international has been Reds’ radar for some time, with some rumours suggesting that they were close to making an offer for his services last year.
However their interest dipped as they eventually managed to keep then wantaway star Suarez at Anfield.
Yet their desire to land the Colombian has not disappeared, with Muriel firmly back on Brendan Rodgers’ wish list
The South American ace has been far from his best this term – hitting four goals in 15 league outings – but he is still admired by Liverpool.
Although Suarez committed his future to his current side recently with a new contract, a switch away from Merseyside during the next window cannot be discounted if they miss out on Champions League qualification.
It’s rumoured that his new deal has a £60m-£70m release clause which could be triggered by a club from overseas.
Real Madrid are known to be interested, and are one of the only teams that can afford such a fee.
The 27-year-old is said to be happy at Liverpool once again after a difficult 2013, but if the club miss out on a top four finish his stance may alter.
Even if Liverpool keep Suarez, Rodgers may still be open to adding Muriel to his ranks, with attacking reinforcements seen as a priority.