Wilkinson acknowledged that being the drop-goal hero of England's 2003 World Cup final triumph does not give him a divine right to a starting place in the Lions Test team for this summer's New Zealand tour.
"It wouldn't sit easily with me to think that I'm there because 18 months ago England won the World Cup and I was the one who kicked the last ball over," he said.
However, Wilkinson added: "I will be very, very disappointed if I don't make it but either way I will do everything I can to help."
Wilkinson watched on earlier this year as Jones enhanced his reputation in a revitalised Welsh side, while he was struggling to overcome a series of injuries.
"The guys on the tour are all fantastic and Stephen Jones is a great player, to name one. They have just won the Grand Slam so I have a huge amount of respect for the guy," Wilkinson added.
"I'm more than happy there are players like Stephen Jones out there. It bodes well for the tour."
Wilkinson is now happy to leave it up to Woodward to decide if he is ready for a Test team place.
"It's just the start of the job getting on the tour, the main bulk of it has still to be done," he said.
"Being competitive and constantly wanting to succeed and be your best, it doesn't seem quite right being a late addition, but some things are out of your control, like some of the injuries which have been difficult to take.
"I don't like to be a last-minute addition or an after-thought, but this year that's been forced on me and I've now got to look to myself to try and prove to those who supported me to try me."