Manager Brendan Rodgers is struggling to agree a deal for the wide man, and are concerned that Benfica have now entered the race for his signature.
The Ghanaian international was understood to be keen on a potential switch to Anfield, although the Reds have been unable to reach an agreement with Porto over a fee.
The Portugese giants are looking for £6million for the 21-year-old, a fee that so far Liverpool have been unwilling to match.
Rodgers is looking to boost his attacking options at Anfield, and sees Atsu as the genuine wide man his side have been missing.
There is still hope that a deal can be struck however, with Porto unlikely to want to sell to a close rival such as Benfica.
Atsu is adamant he wants to leave the club after five years at the Estadio Dragao, and would likely favour a switch to the Premier League.
Liverpool have been busy in the transfer market this summer already, bringing in four new signings including attackers Iago Aspas and Luis Alberto from La Liga.
Rodgers priority has been to try and keep hold of Luis Suarez who is attracting interest from Arsenal, although the Northern Irishman has spoken often of wanting to add exciting attacking talent before the close of the transfer window.
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