On Friday, DC United head coach Ben Olsen confirmed his club's interest in signing the 32-year-old, who has scored 11 goals in all competitions in 2017-18.
Everton boss Sam Allardyce insisted Rooney has not put in a transfer request and Walcott - who joined the Toffees from Arsenal in January - hopes to see his team-mate remain at Goodison Park.
"The 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," Walcott told Sky Sports, with Rooney set to miss Sunday's final game of the season at West Ham due to a minor knee problem.
"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."