Bobby Horan, 51, fears Niall, 18, can't handle consuming alcohol very well.
He said: ''Two beers and he's falling around.''
A source close to the Daily Star newspaper: ''Bobby's been texting Harry as he is Niall's closest friend in the band.
''He knows his son can't handle his drink and so he has asked Harry to keep an eye on him.''
His concern has increased after a number of recent events where Niall has apparently embarrassed himself.
The insider said: ''Niall was completely hammered at the wedding of JLS star Marvin Humes and Saturdays girl Rochelle Wiseman last month, and ended up falling about and saying daft things he later regretted.
''He wasn't much better after One Direction's performance at the Olympics closing ceremony.
''But Bobby trusts Harry and wants him to make sure his son drinks responsibly in future.''
Niall recently admitted that he ''wishes'' he was dating Demi Lovato.
The singer has been linked to the 'x factor' USA judge after they both spoke of their admiration for each other, but he insists there's nothing going on, even though he would like there to be.
When asked if he was romancing Demi, Niall said: ''I wish! No there's nothing going on, but she's a lovely girl.''
Niall - who was speaking in the Virgin Media Louder Lounge at Virgin Media's V Festival over the weekend - was first linked to Demi earlier this year after they both revealed they had crushes on each other.