The talented Argentine could be sold by the La Liga giants to free up funds to spend in January, with key man Antoine Griezmann staying put.
Correa is just 22, and has spent the last three seasons in Spain since signing from San Lorenzo.
Atletico Madrid's Angel Correa
Correa can play in a range of positions, fitting the mould of versatile attacker Liverpool boss Jurgen Klopp admires.
He played last season as a right winger and a striker, but 28 of his 40 club appearances came from the substitute's bench.
This limited his return, scoring four goals and providing eight assists, which included a goal set up in the derby against Real Madrid.
Atletico Madrid's Angel Correa in action
Correa is in need of a move to a club where he can play more regularly, and if Jurgen Klopp can convince him he will get more opportunities then the Reds might stand a chance.
He would fare better played as a striker, with the Reds low on quality options, compared to out wide where they have greater depth.
The Argentine could be a big addition if Liverpool can get him. Here is a look at how fans reacted on Twitter to the transfer rumours...
I've been buying Angel Correa in Fifa for the past 2 seasons, buy him he turns out an 87er rating he must be good #lfc— Paul Mallen (@PaulMallen2) July 11, 2017
Angel Correa... Klopp really has his ducks in a row with targets. Better than Carroll and Adam recommendations back then #Lfc— Brent Brache (@BrentABrache) July 11, 2017
Does anyone believe these that we've offered Angel Correa a contract? Personally I don't because Atletico have a transfer ban. #LFC— Jake (@EmreScreamer) July 11, 2017
And if we do pull off the signing of Correa then I think we say goodbye to one of Origi and Ings for sure #lfc— Chris Burn (@redbhoyburn) July 11, 2017
Hopefully there's substance to the Angel Correa rumours. He's a decent player and will only improve under Klopp— KloppsRedMen (@kloppsredmen11) July 11, 2017
Amazing if we get Correa. 21/22. Klopp can make him the new Suarez. https://t.co/iL7WJ2pAiX— James (@_lfcjay) July 11, 2017