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But the deal nearly came unstuck because of concerns by the English Premier League outfit over the amount it needs to pay clubs in New Zealand for the player's development.
Fulham is a tier-one club in the eyes of world governing body Fifa and guidelines suggest Fulham would need to pay $30,000 annually to clubs Musa played for from the age of 12.
The club baulked at the potential cost, threatening to withdraw the contract offer until a common sense agreement was reached.
There needs to be a balance between getting some money for development and ensuring this does not block a player's ability to be signed by an overseas club, which is still the best pathway for young players in this country.
It is understood Fulham will pay some remuneration to New Zealand clubs for which Musa played, including the Wellington Phoenix, if it signs him beyond the initial six-month contract.
Musa trialled with Fulham after the Olympics and flew to London yesterday to be put through a medical before signing the deal, which needed to go through before the transfer window closes today.
"There was a situation with Fifa in relation to training compensation fees," New Zealand Football chief executive Grant McKavanagh said.
"We have to make sure if people are developing players that there is recompense for that to happen, that's what the rules are put in place for, but we also understand that we have to be flexible and reasonable around that.
''So what has occurred is that an agreement has been reached between the clubs and Fulham, as far as I am aware, and that everything is all go.
"We are not Barcelona and understand that. What we are talking about [with the rules] is someone coming through the Barcelona development system and going across.
''We understand where we sit in the scope of the world. But what we need to make sure we do when we are developing players is that money comes back. We will look at every case and make sure it's fair and reasonable."
It will be interesting to see how Musa fares at Fulham, assuming he passes his medical and signs.
He played only 35 minutes of New Zealand's Olympic campaign when he came on against Egypt but has clearly impressed in his trial.
The 20-year-old has potential - he is quick and athletic - but is prone to being exposed and some do not warm to his attitude on and off the field. It was a principal reason he was released by the Phoenix 18 months ago.
Musa is optimistic of his chances at Fulham, and game time with the reserves will be his initial target.
"Hopefully, I fitted in well," he told the Wanganui Chronicle.
"The clubs in England look for potential. They're a business as well as a football club, so they try to make money off a lot of people.
"The key is to get yourself over there, get your foot in the door, try to show what you've got and try to progress through the grades. Just to get over there and get into the environment is the thing."