HITC Sport understands that the Scottish Premiership champions are closely monitoring the current Northern Ireland boss.
O'Neill is set to hold talks with his employers at the Irish Football Association, who want to offer him just a two-year deal despite them standing on the brink of qualification for their first ever European Championship.
The former Newcastle United and Dundee United midfielder has worked wonders with Northern Ireland, edging them towards France next summer, and his performance at the helm have not gone unnoticed.
Sunderland, who have just parted company with Dick Advocaat, are believed to be considering him, whilst his former club Dundee United are also looking - but it is Celtic who are seemingly heading the chase.
Celtic are currently considering the position of their own boss, Ronny Delia, whose future at Parkhead looks bleak, and so the Glasgow giants are believed to be looking at alternatives, and O'Neill is very much on their radar.
Now the pressure will be on the IFA to try and tie down O'Neill to a long-term deal, otherwise run the risk of losing their highly-rated boss.
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