The Daily Star says Plattenhardt, 26, wants to first cement his place in Joachim Loew's side who start their campaign against Mexico in Moscow this afternoon.
But once football's showpiece is over, Hertha Berlin star Plattenhardt will consider the move to Goodison as Leighton Baines' left-back replacement.
Agent Herbert Briem will then meet Everton officials to sort a deal for the free-kick specialist.
Briem said: “Good left-backs are in demand. But Marvin concentrates on the World Cup first. Everything else will be discussed after the tournament."