Alisson enjoyed a phenomenal campaign in the just-ended Serie A and his market transfer fee skyrocketed for this summer's transfer window.
Liverpool's first choice is Oblak but the Spanish club have slapped a £80million price tag on their goalkeeper which the English club do not want to match.
Not only has the German signed Fabinho from Monaco, but he's working on deals to bring the likes of Nabil Fekir, Moses Simon and Alisson to Anfield.
It's been claimed they will go back in for the Brazilian stopper in the summer but South American football expert Tim Vickery believes competition will be fierce.
"No progress with keeper search for Liverpool", reports the Mirror's David Maddock.
The same article states that the Merseyside outfit are set to be priced out of the deal to sign Atletico Madrid goalkeeper Jan Oblak. Liverpool may be forced to look elsewhere.
"He's is in the next room to me, he is my next rival but I congratulated him and I hope he has a lot of success playing at Manchester United", Firmino added.
"Yes, he asked me and I hope he can come, but I know he has other proposals", he was quoted as saying by Mediaset journalist Andersinho Marques.
It was in the Kiev showdown with Real Madrid that Karius committed two errors, leading to goals for Zinedine Zidane's side.
Firmino says he wishes Fred well at United, but said the rivalry between Liverpool and Manchester United precludes him from wishing Fred too well.
Firmino said: 'Every once in a while I give him a pinch to come to Liverpool to help us and such, but it's with his agents.
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