Suarez is considered to be one of the best strikers to wear a red shirt, bringing the North West giants so close to a Premier League title before leaving for Barcelona.
The Uruguayan has scored 147 goals for the Catalan outfit in just 1919 games, but at the age of 33-years-old and younger players making their way in the team could be set to leave the club.
Juventus were tipped to sign the goalscorer, but ESPN have reported that the Serie A club have made a U-Turn according to reports.
This has prompted former Reds player Steve Nicol to urge Liverpool boss Jurgen Klopp to sign Suarez.
Nicol said: “That would be a great [move]. It completely and utterly makes sense – it’s being smart.
“After you speak to him, you’re going to get a guy who I think is going to be happy to go back and play at Anfield, is going to get sufficient amounts of games to keep him happy.
“He’s quality, he will score goals, he will give you something in the front three that I don’t think they possess.”