They could also look to sign Romelu Lukaku from Chelsea, who has been linked with a permanent switch to Everton, while Mario Balotelli is also believed to be on their radar.
Top spot for Liverpool
This could be a huge summer for Liverpool in the transfer market as they look to consolidate their position in the top four once more, something made much more difficult because of Suarez's departure.
However the fact they were able to secure a fee in the region of £75 million will certainly have softened the blow - and could indeed help them finance a spending spree to launch them into the big time once more.
According to the Express one player they Liverpool have identified to spend some of the Suarez cash on is Di Maria, who has been heavily linked with Manchester United.
Manchester United battle
He's said to be available for around £40 million this summer as Real Madrid look to make way for James Rodriguez - and Manchester United are believed to be leading the race alongside the likes of Paris Saint-Germain and Chelsea.
Other potential targets include Lukaku from Chelsea who has a £25 million price tag on his head, while Balotelli, who has been linked with Arsenal, is also on their radar.
If they do decide to swoop for Di Maria, it will put them in direct competition with rivals Manchester United, who are said to have made him one of their top targets.
Liverpool have also been linked with Lazar Markovic, Alberto Moreno, Dickov Origi and Xherdan Shaqiri.