He outshone current England fly-half Owen Farrell, who is also hoping to be named in the Lions squad on Tuesday.
Lions fixture list
Sat 1 June:
Barbarians, Hong Kong
Wed 5 June:
Western Force, Perth
Sat 8 June:
Queensland Reds, Brisbane
Wed 12 June:
Combined New South Wales-Queensland Country, Newcastle
Sat 15 June:
New South Wales Waratahs, Sydney
Tue 18 June:
ACT Brumbies, Canberra
Sat 22 June:
First Test, Brisbane
Tue 25 June:
Melbourne Rebels, Melbourne
Sat 29 June:
Second Test, Melbourne
Sat 6 July:
Third Test, Sydney
"Young players like Farrell, Toby Flood, Wales' Dan Biggar and Ireland's Jonny Sexton are taking rugby forward. It's their era," said the 33-year-old.
"I want those guys to experience that because they deserve it. I'm digging my fingernails in and hanging on really, and watching these guys is what it's all about."
But Wilkinson, who toured with the Lions in 2001 and 2005, could be named alongside, or at the expense of, those players when head coach Warren Gatland announces his selection on Tuesday for this summer's tour to Australia.
One factor against him is Gatland's
preference to leave with his whole squad together
on 27 May, but Toulon are likely to be involved in the French Top 14 final on 1 June, the same day as the Lions' opening match against the Barbarians in Hong Kong.
The Lions face a three-Test series against the Wallabies, with the first Test in Brisbane on 22 June.
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