The Bhoys are currently closing in on a domestic treble, but a dark cloud is looming as Tottenham look closely at Postecoglou.
Postecoglou is on a 12-month rolling contract at Celtic and could walk away from the Scottish giants to answer the call from Premier League side Spurs.
Celtic are claimed to now be shortlisting potential replacements and it has been claimed that West Ham boss Moyes could be firmly on their agenda.
Moyes, the current Hammers boss, is expected to be amongst the front-runners if Celtic do need to appoint a new boss.
The Bhoys are in the chase for a domestic treble and they will face Inverness in the Scottish Cup final this weekend.
Meanwhile, Moyes’ West Ham will square off against Fiorentina in the Europa Conference League final on 7th June.
It remains unclear whether the Hammers manager would be interested in taking on the Celtic job if the opportunity arrives.
