The Stromsgodset player has impressed for his club since making his first-team debut in April.
He has since gone on to make 14 appearances for the Norwegian outfit, scoring three goals and setting up six more.
"This is a dream come true," BBC Sport quotes Odegaard as saying. "I am shocked."
Odegaard, who has previously trained with Bayern Munich and Manchester United, will become his country's youngest ever international if he plays in the friendly in Stavanger, breaking Tormod Kjellsen's 104-year-old record.