The 22-year-old has been with the London club since the end of the January transfer window.
Odegaard was impressive in his first start for the Gunners as they beat Leeds United 4-2 at the weekend.
“But for now I am just focusing on doing my best this season and helping the team as much as possible.”
The Norwegian also expressed his contentment with playing in north London in an interview with the club’s website.
“It’s a bit different but I think I am adapting pretty okay,” Odegaard said. “The way they took me into the team – my teammates – and how they treated me, as well as the manager and everyone in the club, they helped me since the first minute.
“I feel really comfortable and a part of the team, so it’s been easy to come in to this team because of the way they are and the way they treated me. I’m just really happy to be here and I’m proud to be a part of this team.”