Reports suggested that the teammates were to compete behind closed doors.
However, the former England lock has said that the claims were "made up".
"The media have made that up," Johnson told reporters. "We know what we're doing.
"It's a nice little story to write [but] we will decide who is going to take them."
Despite having a better record behind him, Wilkinson has missed 11 out of 20 kicks in the current World Cup campaign while Flood has only missed three out of 13.