The 31-year-old Nene was dropped from the squad for the last three league games after arguing with club officials during the 2-1 Champions League home victory over FC Porto.
Coach Carlo Ancelotti said last week Nene could have made the squad for the home clash against Olympique Lyon if he had not suffered a calf injury, but the player published a picture of himself ice-skating on the internet.
"It's a hard decision to make but I think the time has come for me to follow a new path in my career," Nene was quoted as saying on his official website on Wednesday.
"I think we will reach a consensus and [I will] be released from the remaining contract compliance," he added.
PSG declined to comment.
Nene was the French league's joint top-scorer last season, helping the wealthy club finish second with 21 goals.
The Brazilian, who has played 79 league games for the capital club, has only appeared nine times in Ligue 1 this season, scoring one goal and setting up four.
Media reports have linked him with AC Milan, Turkish side Galatasaray and Brazilian clubs including Flamengo.
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