And his impressive midfield performances have drawn attention from the Premier League big boys, according to .
England have already snapped up the teenager - who is eligible to play for Denmark - for friendlies against Brazil and South Africa ahead of next month's Under-17 World Cup in India.
But that would have come as no surprise to Fulham boss Slavisa Jokanovic, who predicted: "I expect he can be an important player for our club in the future."
O'Riley operates as a playmaker and is winning fans over with his technical ability and sweet left foot.
Arsenal are looking to replace their summer losses after youth product Chris Willock and highly-rated kid Nathan Tella joined Benfica and Southampton respectively.
Man City, meanwhile, are on the lookout for cheap, English talent to make up their homegrown quota.
Manager Pep Guardiola said: "I would like to have English players. People don't believe me but I would like them.
"But they are so expensive. I would like to play with them.
"When I was in Barcelona and Germany I liked to play with the locals, it's special, but sometimes it is not possible - the market is the market."
He added: "That's why the club has worked with the academy for a long time to be thinking about the next years, with me, without me - hopefully with me."
But City must tread carefully as they are set to be investigated by Fifa for breaching regulations on signing young players.