The attacker, who has 76 goals in 302 appearances for the club, is not happy with his manager Carlo Ancelotti.
The pair have a tense relationship, which is on the verge of breaking entirely.
According to Corriere dello Sport, Insigne has a £60 million value.
Many top clubs have enquired about the winger, with the Reds and Blues credited with the most concrete interest.
Insigne is 27 and has a contract until summer 2022.