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Should he move to Liverpool, he is already being tipped to bring several of his current players with him.
Liverpool's next manager will work with FSG's head of football and new sporting director Richard Hughes to identify transfer targets, while decisions will also need to be made over the futures of a number of key players this summer.
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Mohamed Salah is expected to be the subject of fresh interest from Saudi Pro League clubs, with his contract up at the end of next season.
It is claimed that should Chiesa impress with Italy this summer, his agent may look for a hike on his wages with Juventus, or tout him around to other clubs in Europe.
Furthermore, any Liverpool interest is likely to be dictated by whether Mohamed Salah remains at the club.
Liverpool.com says: Salah is again likely to be the subject of interest from Saudi Pro League clubs this summer and with his contract up in 2025, a decision will have to be made, one way or another.
His pace makes him a real threat and if he can add some more goals to his game, he would be an excellent addition.
Luis Díaz
Liverpool winger Luis Díaz wants to join Barcelona this summer, reports Spanish publication Sport
Diaz still has three years remaining on his Anfield deal but is said to face an uncertain future.
According to The Telegraph, Liverpool is likely to make a decision over the Colombian in the summer and FSG will either offer him a new deal or look to move him on
Liverpool is likely to demand around $93m (£75m/€87m) for the winger this summer.
Liverpool.com says: Few Liverpool supporters would agree with Luis Díaz being sold this summer but a big-name exit may be needed to fund spending in other areas