The 35-year-old has made over 300 appearances for PSG after joining from AC Milan in 2012.
But according to L’Equipe his time at the club is coming to an end and he has been told by sporting director Leonardo that his contract will not be extended.
There has been speculation that Silva could return to Milan or move to the Premier League to reunite with Carlo Ancelotti at Everton.
The pair worked together at PSG and Milan, and Silva has spoken off his fondness for the Italian.
“I’ve worked with a lot of coaches in my career, but one man stands out, and that’s Mr Ancelotti,” he said in 2013.
“It wasn’t easy for me to find my feet when I first arrived in Europe. When I joined AC Milan I didn’t play for six months. But I was training under a great coach in Carlo Ancelotti. I can’t stress how important those six months were – they changed my life.”
He will play in the Champions League in August with PSG before departing.