It's emerged this week that Gomes has turned down a new contract offer from United amid interest from Barcelona.
However, Don Balon says Real are also in contact - with Ronaldo taking a personal interest.
Gomes, while an England youth international, has a Portuguese father - a former pro footballer - and has been followed closely by Ronaldo.
Ronaldo has spoken glowingly to Real president Florentino Perez about Gomes' potential and urged him to move for the midfielder should he become available.
Barca, meanwhile, have told Gomes' camp that they see the teen as skipper Andres Iniesta's eventual heir.