Perisic could leave Inter after shining in Serie A this season.
And Italian newspaper Gazzetta dello Sport claim the playmaker could be set for a move to Anfield.
Jurgen Klopp is hoping his personal knowledge of the player can help Liverpool beat Chelsea to his signature.
Klopp coached the player at Borussia Dortund, with Perisic winning the Bundesliga title under the Reds boss back in 2012.
Liverpool want to sign Ivan Perisic
Emre Can was reportedly scouted by Juventus
Will Ferrell spotted in the crowd as Swansea beat Liverpool
Sun, January 22, 2017
Will Ferrell was spotted in the crowd at Anfield as Liverpool suffered a 3-2 defeat at the hands of Swansea City
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Will Ferrell was spotted enjoying himself at Anfield as Swansea beat Liverpool 3-2
Juventus sent scouts to watch Liverpool midfielder Emre Can, reports claim.
Can has struggled to nail down a starting spot in Klopp's XI this season
And Italian newspaper Corriere dello Sport claim Juventus are eager to lure him away from Anfield.
The Germany international was said to have been scouted during Liverpool's 1-1 draw with Manchester United last week.
But Klopp could block any potential transfer and postpone a decision on his future until the end of the season.
Philippe Coutinho looks set to stay at Liverpool
Journalist Guillem Balague believes Barcelona will not be buying Philippe Coutinho.
Coutinho has regularly been linked with a move to the Nou Camp throughout his time at Anfield.
But Balague cannot see a transfer materialising due to the fact the La Liga giants do not need him.
“I don’t think so," he said when asked about Barcelona's reported interest.
“There has been no real interest from Barcelona for the Liverpool forward.
“I know Rivaldo has spoken about it but it doesn’t make sense because they see him as a forward and the front three will be the front three next season.”