The 17-year-old has shone this season for the Scottish side, and Real Madrid scouts were reportedly at Tannadice on Wednesday to watch the youngster in a 4-1 League Cup win over Partick Thistle.
Ironically, the young forward has been nicknamed 'Mini-Messi' by team-mates in honour of Barcelona's Argentine superstar, with Gauld's diminutive stature, brilliant dribbling, creative play and even his haircut all inviting comparisons with the great man.
The Scotland U19 player stands just 5'5" tall, but his extraordinary talent earned him a debut for Dundee United on the final day of the 2011-12 season - when he was just 15 years old.
Gauld played 10 matches for the club last season - prompting then-manager Peter Houston to praise him in glowing terms: "He can go past people as if they're not there."
Since then Gauld has broken into the first team, and team coach John Rankin - who came through the youth system at Manchester United alongside the likes of Darren Fletcher - has insisted that Gauld is good enough for the Bernabeu.
“Ryan has a massive future,” he was quoted as saying. “The talent in the boy is incredible. If he is being linked with Real Madrid at that age, then it wouldn't surprise me - it really wouldn't.
“He is so level headed and if anyone deserves it, it would be him. I don't know if someone is hyping it up or someone is just trying to make a story, but I hope for the sake of the boy it's true," he added.
“It certainly would not surprise me if he moved on to a big club. You want to see him doing well. He is so grounded and I hope for his sake and for the sake of the club - and a right few million - that it's true.
"He definitely has the potential to have the rest of us sitting in an armchair in a few years with the feet up saying: ‘I played with him.’ You put your chest out and feel proud to say it."
Rankin added that he has another player at the club who could also become a star: defender John Souttar.
"I know everyone is talking about Gauldy, but I see no reason why John Souttar can’t reach that level as well," he added.
"I don’t know another centre-back who would try backheels, drag-backs and nutmegs on guys on the edge of their own 18-yard box."