Wilkinson, whose playing career finished in 2014, has yet to agree to Jones' invitation.
It was Wilkinson's late drop-goal that helped England beat Jones' Australia in the final of the 2003 World Cup.
"We would like to get Jonny involved, but he's quite a private person. We are having chats about it," Jones said.
"I saw him down at Waitrose shopping with a beanie over his head. I had coffee with him," added Jones, who has appointed Steve Borthwick, a former England team-mate of Wilkinson's, and Paul Gustard as forwards and defence coach respectively.
Wilkinson won 91 England caps, is his country's leading points scorer and is one of just five men to score 1,000 points in international rugby union, with his total of 1,246 second only to New Zealand great Dan Carter.
"After we had coffee he went and did a kicking session, and he doesn't play any more," said Jones, who succeeded Stuart Lancaster following England's early exit from the 2015 World Cup.
The 55-year-old Australian also revealed that he picked up ideas from Bayern Munich manager Pep Guardiola when the pair met last November.
"Pep is a big rugby fan. He studied rugby and European handball to look at how you move the ball into space," said Jones.
"We talked about his philosophy and about how you move the football into space, because in rugby, once you get away from the set-piece, it's like football."
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England head coach Eddie Jones wants World Cup winner Jonny Wilkinson to be part of his coaching team after a chance meeting in a supermarket.