Walcott, however, told Sky Sports News that Rooney's legacy in the Premier League merits him a stay in the top flight.
"he legacy he has brought to the Premier League, the goals, the trophies, everything he has done at Manchester United, England and here, he is an incredible player," the 29-year-old said.
"Obviously I'd love him to stay, I remember having a conversation with him on the phone, he was one of the main players who got me here, so I am grateful for that, definitely.
"But if he does choose to go on I just need to wish him all the best really, him and his family. He doesn't need to prove anything to anyone anymore. However, let's wait and see. Like I said, I'd love him to stay here."
Rooney is expected to miss Everton's final game of the season against West Ham United after picking up a knee injury.