It has been reported that the 35-year-old would remain at PSG, but a contract renewal is now looking less likely.
Silva is a free agent on June 30 when his four-year contract expires.
And according to Italian source TMW, Carlo Ancelotti’s Everton have made their ‘first approach’ to his representatives.
Silva’s former club AC Milan are in the background, but have yet to make any proposal.
It is claimed that Everton could make a concrete offer to the Brazil legend in the coming weeks.
Silva worked with Everton boss Ancelotti when the Italian was in charge at AC Milan and PSG.
And in a 2013 interview, he hailed Ancelotti.
“I’ve worked with a lot of coaches in my career, but one man stands out, and that’s Mr Ancelotti,” Silva told beIN Sport.
“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.”
Although now 35, Silva’s experience and quality would be a big asset to Ancelotti’s project at Goodison Park.