Wilkinson kicked a conversion and two penalties in a 23-16 defeat at Gloucester on May 8, but more importantly proved his form as well as fitness after a horrendous run of injuries which some feared would end his career.
Woodward said: "Against Gloucester, Jonny had a fantastic game.
"Phil Larder did the stats and said Jonny put in 19 tackles out of 19 attempts.
"You do have to go a certain degree on form and reputation, but if Jonny had had a poor game against Gloucester I wouldn't have picked him because of the three guys already in the squad.
"But because he played so well in that game, I was happy to put him in and I have no doubt he will compete very, very strongly for a Test place."