The 70-year-old crooner - who has three grown-up children with first wife Isabel Preysler and five kids with current spouse Miranda Rijnsburger - thinks teaming up with the British boy band would impress his 13-year-old daughter Cristina and Victoria, who are both fans of the 'Little Things' stars.
He told fansite OneDirectionJoy.com: ''My daughters would be very happy if I could do something with One Direction. But who knows?''
And even if Julio - who is the father of 'Hero' hitmaker Enrique Iglesias - doesn't get to work with One Direction, he has a string of other pop stars on his collaboration wish-list, though he knows it may not be easy to make them happen.
He added: ''I promise that in a year I will surprise everyone with music made with a young generation of people.
There are currently five separate teams working on 'Game of Thrones' projects at HBO.
She's a big fan of the band and this week she got to perform with them.