The 24-year-old’s deal expires in 2025 but talks are progressing well over fresh terms, which are expected to see him commit his future to the club for at least a further two seasons.
Ødegaard is also set for a significant increase on his £120,000-a-week wage to reflect his form and improved standing since first joining the club in January 2021.
Ødegaard was named Arsenal captain last summer and has scored 26 goals in 110 appearances for the club.
He refused to be drawn on his contract situation when asked earlier this week while on international duty with Norway, who he also captains.
Ødegaard said: “I don’t have much to say, apart from the fact that I am very happy at Arsenal and I hope I can be there for a long time.
“Beyond that, I have no comment right now. Now, it is the national team that is in focus.”
Arsenal take on Everton on Sunday in their next game.