The brothers have barely spoken since the former footballer’s betrayal was revealed, but it is understood that Rhodri has agreed to attend Ryan’s bash in Manchester.
The ex-United winger plucked-up the courage to phone Rhodri and apologise earlier this year – and the pair were spotted chatting in a Manchester bar at Easter.
Rhodri, 38, has previously said he would only help to repair the relationship if his brother made the first move.
It now appears he has agreed to attend the New Year’s party, where Ryan Giggs’s wife Stacey Cooke and their two children could be in attendance.
It is expected to take place at the star’s £4million mansion in Worsley, Manchester, or at a nearby restaurant.
A source told the Daily Star Sunday : “Both the lads want to patch things up and have done for some time – but neither would really make the first move.
“In the end they’ve come to the conclusion that life’s too short, and what has been done can’t be changed now.”
Details of Ryan’s betrayal unravelled in June 2011 – when Rhodri’s wife Natasha revelaed she had been having an eight-year affair with the United icon.
Natasha also claimed she had aborted Ryan’s baby shortly before marrying Rhodri in Las Vegas.
Earlier in 2011 Ryan, 42, had tried to stop The Sun from revealing his secret relationship with former Big Brother star Imogen Thomas.
The six-month affair was exposed despite the ex-footballer splasing-out on a £150,000 gagging order against Imogen.
But Ryan’s adultery was exposed after a Twitter campaign eventually led to an MP naming in parliament.
Since splitting with Natasha, Rhodri has had a baby son with 24-year-old Ashleigh Turner.
Natasha, 32, had a son with a new partner last year.
As pressure mounts on Manchester United manager Louis Van Gaal after seven games without a win, Ryan Giggs could soon become the Red Devils boss at least on a temporary basis.