Ireland's assistant manager was the short-odds favourite for the Parkhead role but will remain with the Boys in Green after declining the position, the FAI have confirmed
Keane was the strong favourite to succeed Neil Lennon in the Parkhead hotseat after informal talks last week with Celtic owner Dermot Desmond but he will instead continue to work alongside Martin O'Neill with the Irish team.
The Football Association of Ireland released a statement on Monday afternoon confirming that Keane would travel with the Ireland squad to America as planned on Wednesday for their two friendlies against Costa Rica and Portugal.
The statement reads: "The Football Association of Ireland today [June 2] confirmed that Roy Keane will travel with the Republic of Ireland squad to the US after he decided not to pursue the informal talks that took place with Celtic any further.
"The Republic of Ireland squad will gather again in Dublin on June 3 before travelling to New York on June 4."
The new favourite to take over at the Scottish champions is former West Brom manager Steve Clarke while Malky Mackay and Owen Coyle are also in the running.