Manchester United striker Rooney is recovering from a knee injury which has sidelined him since 13 February.
England manager Roy Hodgson said his captain remains a major part of his plans in the build-up to Euro 2016 this summer.
Shakespeare, however, believes Vardy should be picked ahead of Rooney.
“I would love to be in a position to choose between him and Rooney,” he said. “My money, at the moment, would go to Jamie purely on form.
“When we brought him to Leicester we told him he had the attributes to go as far as he wanted. I don’t think he really believed it.
“We’ve seen him go from strength to strength and I’d love to see him play down the middle for England in the Euros and actually do something for his country.
“By that I mean get as far as we possibly can.”
Adrian Chiles will be live in Leicester Market from 10:00 BST on Tuesday, looking at what Leicester City’s incredible season is doing for the city. He will speak to fans and former Leicester players Steve Walsh, Muzzy Izzet and Gary Lineker.