The 25-year-old shot-stopper is now under contract with Italian side AS Roma, but there is not a secret that Real Madrid want him; in fact, reports from last week indicated that Alisson has already reached an agreement with the player.
Sky Sports News reporter O'Connor claimed that the Merseyside outfit are resigned to missing out on the Brazilian shot stopper.
Alisson, also called Alisson Becker, made 37 appearances in Serie A for Roma this season, conceding just 28 goals and keeping a total of 17 clean sheets.
"Liverpool don't see any need to go in for him".
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"They were interested", O'Connor told the Transfer Talk podcast.
The Italian outlet CalcioMercato have speculated this evening that Perez will also look to launch a bid for Roma goalkeeper Alisson who is likely to have a price tag on his head in the region of 80 million euros (£70m).
On Sunday evening, Alisson made his World Cup debut with Brazil against Switzerland and impressed with his distribution from the back.
It looked like Liverpool were set to miss out as TeamTalk are citing a report from El Mundo Deportivo that claims the Brazilian global has agreed personal terms with Real Madrid over a five-year contract ahead of a proposed move to the Bernabeu.
With a World Cup campaign underway that could cause that transfer fee to swell further, Steve Nicol believes Liverpool should pay whatever Roma want if they believe it to be worth it.