Brendan Rodgers is expected to become Leicester City's new manager after Celtic has given him permission to speak at the Premier League club.
Northern Ireland followed a normal training on Monday but the Fox want to install as soon as possible the successor of Claude Puel.
Rodgers won seven of seven national trophies in his time in Glasgow.
First-team coach John Kennedy is expected to coach Celtic on Wednesday's Premiership tour against Hearts.
Former Liverpool boss Rodgers curtailed a BBC interview about the vacant post in Leicester after Celtic's victory over Motherwell on Sunday.
The champions are eight points ahead of their nearest rivals, the Rangers, in the Scottish Premiership, as they run after an eighth straight title.
Rodgers has won two league titles, three Scottish League cups and two Scottish cups since arriving at Parkhead in the summer of 2016.
They reached the knockout stages of the Champions League in their first two seasons, but were eliminated in the third qualifying round by AEK Athens this weekend, in a climate of unrest between Rodgers and the United States. Celtic board of directors for not having strengthened its staff last summer.
"The news that Celtic fans had dreaded" – analysis
Chris McLaughlin, sports correspondent for BBC Scotland:
This is the news that Celtic fans had dreaded. Since he took office in 2016, he has delivered everything in his country – the double hatch was secured at the end of last season and the club was on the verge of making it a triple treble. .
But there was always a feeling that the former Liverpool boss wanted to try his luck once again in the high flight of English football. The suggestions that he was not getting support from the meeting room that he was looking for may have also precipitated his release – but that leaves Celtic looking to replace one of their brightest managers.
Phil McNulty, Editor-in-Chief of the BBC Football
Rodgers has rebuilt his reputation in Scotland after his ultimate failures in Liverpool and certainly does not lack personality or charisma.
Aged 46, American football is also attractive, attacks football and shares the penchant Puel for the promotion of young talents. And after three years and seven trophies – so far – Rodgers may have the feeling that the time has come to leave.