His father Hans Erik Odegaard said the teenager, who has spent time with Manchester United and Bayern Munich, has been the subject of over 30 enquiries from Europe's top clubs.
"I can't name the clubs, but almost regardless of who you name, they have been in contact with us," Odegaard senior told newspaper Verdens Gang.
His son has electrified Norwegian football since making his senior debut in a top-flight match against Aalesund in April, becoming the youngest player in the history of the Tippeligaen.
Odegaard went on to become the youngest scorer in the Norwegian league when he netted the final goal in a 4-1 win over Sarpsborg.
He followed that up with a stunning performance against Sandnes Ulf, scoring one goal and creating two more in a 3-1 victory and prompting comparisons in style with Barcelona's Lionel Messi.
With his quick, mazy dribbling and incisive passing, the left-footer's play bears more than a passing resemblance to the diminutive Argentinian, and the question for Norwegian champions Stromsgodset will be how long they can hold on to him.
Verdens Gang reported that clubs such as Barcelona, Manchester United, Manchester City, Juventus, PSG and Ajax have visited Stromsgodset's Marinelyst home ground to see Odegaard in action.
"We want Martin to develop," said his 40-year-old father, who has also played professionally in Norway, adding that it would be impossible to visit all the clubs that have been in contact.
"That (development) has been the focus over the years. If you start to think about other things, I think the development comes to a halt," Odegaard said.
(Reporting by Philip O'Connor, editing by Ed Osmond)
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