"I want to extend his contract and I didn't wait until after Saturday's game to begin discussions", said Boudjellal.
"It's actually my main priority but I'm not very worried.
"The player wants to stay and his president wants to keep him at any price so we should come to an agreement quite quickly."
The England outside-half has made nine appearances for the Lions, racking up 116 points and staring during the 2001 tour to Australia.
After struggling with injuries, the all-time highest international points scorer made the move to the south of France in 2009 and has made a huge impact at the Top 14 club.
He helped them to the Amlin Cup and Top 14 finals last year leading to their qualification for this season's Heineken Cup.
Wilkinson has continued to pull-the-strings this season and scored 23 points in Saturday's 28-16 win over champions Clermont Auvergne.