Such is the focus on the midfielder that 35 scouts from some of those teams -- including Manchester United and Liverpool of the English Premier League -- came to watch him at a recent Under-21 match.
"In the beginning it was unreal and a little bit surreal that all these clubs wanted Martin, but it's strange what you can get used to," his father Hans Erik Odegaard tells CNN. "Almost every top European club has been in touch."
His international debut is not Odegaard's only record-breaking feat this year. In April he became the youngest player in the history of the Tippeligaen when he made his debut for Stromsgodset in a top-flight game against Aalesund.
He followed that up by scoring the fourth goal in a 4-1 win over Sarpsborg to become the youngest scorer in the Norwegian league.
Former Norway international Morten Gamst Pedersen has described Odegaard's potential as "unbelievable," while manager Ronny Deila -- who gave the teen his Stromsgodset debut before joining Scottish club Celtic -- says he can "become the best in the world."
Odegaard's father, a former footballer at Stromsgodset and Sandefjord, recalls the moment when he realized his son might have what it takes to play professionally.
"I saw from a very early age that 'he had the feeling,' but I remember very well when I knew he'd be quite good," he said.
"I was still playing and Martin must have been no more than eight. I was out on the pitch running some intervals. He was, as always, with me. When I was finished I wanted to go home, but we couldn't before he had done 50 more shots (at goal).
"Then I understood he also had a talent for training and that is the most important talent you can have."
"Quite good" probably doesn't do Odegaard's myriad talents justice, given he has been compared to Lionel Messi or -- closer to Scandinavia -- the legendary Denmark international Michael Laudrup, who played for Juventus, Barcelona and Real Madrid.
"I'm sure you can compare him with many, but I don't like to do that," reflects Hans Erik. "Those players are and were so good and Martin is at the start of his career."
Former Monaco chief executive Tor-Kristian Karlsen, who is Norwegian and has watched Odegaard's progress over the last few months, is a fan.