The 16-year-old has been linked to nearly every major club between Manchester and Real Madrid in recent weeks, with reports now suggesting the European champions are close to securing his services.
Ødegaard landed in Madrid late on Tuesday with his father and agent to hammer out a deal, and the club have already printed up a number 16 shirt in preparation for the transfer of the talented Norwegian, newspaper VG reports.
"There's been a lot of noise surrounding Martin and we decided to not contribute to it by refusing to feed the rumours," his father Hans Erik Ødegaard, himself a former professional, told AFP.
"The only thing that matters is that he can develop as a footballer," the father added.
Ødegaard, already a Norwegian international, fuelled speculation about a move from his hometown club of Strømsgodset by going on a grand tour of Europe's football giants in England, Germany and Spain around his 16th birthday on December 16th.
While the professed Liverpool fan trained at and carefully inspected facilities, press reports had him linked one day with Ajax Amsterdam and the next to Real Madrid in a €12 million ($14.3 million) deal.
He could also plump for Bayern Munich, whose president Karl-Heinz Rummenigge has named him "the talent of the century."
Like Barcelona forward Neymar, another former wonderkid, the Scandinavian is spoiled for choice. "He has a future wherever he goes," said Barcelona coach Luis Enrique.
The Catalan club would like Ødegaard but they are banned from signing players until January 2016 after breaching rules on signing under 18s.
More than 30 clubs have expressed an interest: Manchester United and City, Arsenal and Borussia Dortmund are also on the list. But English Premier League leaders Chelsea are not among them.
Chelsea manager Jose Mourinho said he would not get involved in an "auction" for the teen.
"I have heard from him and he can go to 25 clubs. I want to know what club it is going to be, but we will not go into battle with all these clubs."
It has been less than a year since the left-footed Ødegaard's talent first came to light.
In April 2014, he started playing for Strømsgodset, in his home town of Drammen, where he became the youngest player and scorer in the Norwegian Premier League. In 23 games he has five goals and seven assists under his belt.
Videos of the young player running rings around opponents have gone viral and soon came to the attention of Norway's national team.
In August, Ødegaard wore Norway's red and blue shirt for the first time in a friendly against United Arab Emirates, aged just 15 years and 253 days, a national record.
In October, he became the youngest player ever to appear in a European Championship qualifier, coming on as a substitute in a match against Bulgaria.
"He has developed enormously in a short time. He brought down barriers that I think neither he nor anyone else imagined would fall," Norway manager Per-Mathias Høgmo told the Aftenposten daily.
"His way of playing, his talent, his ability to make choices and think, all of this is impressive," he added.
However, even though the appeal of joining a Champions League club may seem irresistible, some are recommending Ødegaard, technically still under contract with Strømgodset for the 2015 season, wait to gain more playing time and even more centimetres in height.