The Whites were linked with a deal for the central midfielder throughout the summer.
Leeds United, who were relegated from the Premier League last season, should aim for an automatic return to the top tier of English football.
The Whites spent three seasons at the top of the Premier League and are now back in the Championship, battling for promotion alongside Leicester, Ipswich, and Sunderland.
£10m
German boss Daniel Farke was snapped up, after his exit from Bundesliga outfit Borussia Monchengladbach, to lead the charge and he arrived with a proven track record at this level.
Leeds reportedly offered a fee of around £10m for the Denmark U21 international but were unable to convince the Scottish giants to part ways with their midfield maestro.
Hoops boss Brendan Rodgers later revealed that he was determined to keep hold of O’Riley after the club had already cashed in on Jota and Carl Starfelt, and the ex-Liverpool manager was not keen on losing another one of his key players.
The Northern Irish head coach did, however, go on to say that he could never rule out a move if the player decided that they would like to move on, although that was not the case with the Danish gem this summer.
This suggests that there is scope for Farke to attempt to convince O’Riley that a switch to Elland Road is the best next step in his career, and Leeds challenging for automatic promotion when the January window opens could help to do that.
O’Riley’s outstanding performances for Celtic as an attacking threat from midfield imply that he has the potential to evolve into a Buendia-type player for the Whites manager, albeit in a somewhat different capacity.