But Wales fly-half John, who was dubbed 'The King' on his return from the only Lions Test victory in New Zealand in 1971, insists Woodward cannot afford to gamble on players' fitness.
"If you take him, you have to play him in the early games just to find out if he is up to it," John told Wales on Sunday. "If he isn't, what a waste of time.
"You haven't games to waste on the modern tours, which are so short compared to what they were in the amateur era."
John believes Woodward should instead pick in-form Welshman Stephen Jones.
"I think Clive has to go on form," he said.
"If you look at Stephen Jones and what he has done this year, you just cannot compare. Steve has been fantastic."
He added: "Even if Wilkinson was around, I would have to say that Stephen is the man."