The 18-year-old has impressed for the Easter Road side’s development squad in recent years but has fallen down the pecking order with the recent arrival of fellow centre-half Kos Sadiki, who has partnered Kevin Waugh in defence for most reserve games this term.
O’Connor signed his first professional deal with Hibs in January 2017, and captains the club’s Under-18 side, but is yet to break into the first team at Easter Road.
He has also featured for Scotland at Under-16 and Under-17 level.
He was an unused sub as Hibs defeated Highland League outfit Turriff United in the Irn-Bru Cup third round in September 2016.
With his contract due to expire in the summer, O’Connor will feature for Burnley Under-23s in a friendly match against their Huddersfield Town counterparts on Wednesday.
The Terriers are also understood to be interested in O’Connor, while English Championship side Brentford are also keeping tabs on the situation.
The youngster is expected to hold talks with all three clubs over the coming days.