The ex-England international has been in talks with the Major League Soccer side over the past fortnight regarding a summer switch, just a year after rejoining his boyhood club from Manchester United.
Debate surrounding Rooney's future has dragged into Silva's tenure, with suggestions that the 32-year-old will now consider remaining at Goodison Park following the exit of Sam Allardyce.
Silva would not give too much away when probed on the topic during his unveiling on Monday afternoon, telling reporters: "It's something that had started when I arrived. We will talk with him. We need to understand everything.
"He is a club legend. The door is open anytime for him to return. We'll talk and see what is happening. It's Wayne's decision."
Rooney started 32 games during the 2017-18 campaign and has a year left to run on his existing Everton deal.