Social media footage circulating online appears to show the Northern Ireland international using a derogatory term in reference to Hoops fans.
The video starts with a member of the public appearing to want a photo with the 35-year-old. With the clip being filmed and as the pair pose, the man seems to state ‘Up the Celts’, prompting Lafferty to step away and make a comment as he walked off.
Lafferty could now face disciplinary action from the Scottish Premiership club after the Ayrshire side confrmed they are looking into the incident.
A club statement read: “Kilmarnock Football Club are aware of a video circulating online which appears to show a member of our playing staff using language of a sectarian nature.
“The club finds all forms of discriminatory behaviour completely unacceptable. The matter will be investigated by the club.”
Lafferty, who has earned 85 caps for his country, is currently on international duty with Ian Baraclough’s side ahead of Nations League matches against Kosovo and Greece.
He rejoined Kilmarnock for a second spell in January after a short stint with Cypriot club Anorthosis Famagusta.
He spent two successful spells at Rangers (between 2008-2012 and 2018–2019), winning three Scottish Premiership titles and also counts Hearts, Sunderland, Burnley and Norwich City among his former clubs as well as spells in Norway, Switzerland, Turkey and Italy.