The Manchester United veteran phoned Rhodri, 34, and said allegations he slept with his younger brother’s wife Natasha were untrue, the Sun newspaper reported.
But her father, Phil Reade, told the newspaper: “Rhodri is not going to take Natasha back.
“I feel for Rhodri, I really do, because he’s been a real gent as far as Natasha is concerned.
“I’ve tried to speak to Rhodri but he hasn’t replied to any of my messages yet. I can only assume it’s because he’s too upset.”
A friend of his daughter was quoted at the weekend saying she had an eight-year affair with Ryan Giggs.
The claims emerged after the 37-year-old Welshman, who has two children with his wife Stacey, 32, obtained a court order banning publication of details of an alleged affair he had with Big Brother housemate Imogen Thomas.
The injunction was breached in the House of Commons after details appeared on the internet, although Thomas is still barred from speaking about it and is planning to challenge the gagging order on her.
She reportedly said of the new allegations: “I thought I was special. It goes from bad to worse.”
Giggs was awarded an OBE in 2007 and is one of the Premier League’s most successful footballers.
The News of the World reported at the weekend that Natasha Giggs had told friends she met the footballer in 2003, the same year she met his brother.
She alleges that their affair carried on even after she married Rhodri Giggs last September.
Meanwhile, Big Brother star Imogen Thomas has vowed that she will never hook up with a footballer again.
The glamour girl was recently pictured in a Manchester United kit for an ad campaign for a firm of bookies.
And in a photoshoot for lads mag Nuts, she said she would draw the line at ever dating a football player again.
She denied reports she had been seeing Spurs striker Jermain Defoe, and said: “Why on earth would I be out with Jermain Defoe after all I’ve been through, that’s not in my interests. I’m not ready to look now.”
Asked whether she would consider hooking up with a footballer, she said: “No, never.”