The Arsenal midfielder played the full 90 minutes as England extended their unblemished record in Euro 2016 qualifying on Saturday with a 3-1 win over Slovenia, a fourth successive victory.
The London club face a huge Premier League clash with Manchester United on Saturday and Wenger would no doubt like the 22-year-old to play a peripheral role in Glasgow to keep him fresh.
However, Wilshere is relishing the chance to face their biggest rivals after a stirring speech from coach Roy Hodgson.
"He's already given us a speech about England-Scotland and told us that back in the day it was the highlight of the season," said Wilshere.
"We know what we're walking into and we'll be ready. It's going to be a great atmosphere.
"I want to play. I'm desperate to play. They are the games that every England player wants to be playing in."
England have not faced Scotland on Scottish soil since 1999, a 2-0 win for the visitors, but both sides have a victory in the last two meetings at Wembley.
