The 33-year-old kicked all of the French giants' points as they beat Saracens 24-12 to earn a spot in the Heineken Cup final on Sunday at Twickenham.
Warren Gatland will announce his squad for the tour on Tuesday, but Wilkinson is not expecting his name to be read out.
"The Lions is difficult for me because it's not at all that I wouldn't consider it - it would be fabulous. It's up there with the most amazing experiences you can get in rugby," Wilkinson told Sky Sports News.
"I want those guys to experience that because they deserve it. I'm digging my fingernails in and hanging on really."
Wilkinson last appeared for the Lions in 2005.