The 22-year-old joined the Hoops from MK Dons for just £1.5m in January 2022 and has since established himself as a star player at Parkhead.
O'Riley has scored 14 goals and registered 20 assists in 85 appearances for Celtic across all competitions, including six goals and four assists in 13 games so far this season.
The Hounslow-born midfielder was recently rewarded for his exceptional start to the new season with a senior call-up to the Denmark national team squad earlier this month – eligible via his mother's side of the family – although he is still waiting to make his debut.
O'Riley most recently put in a man-of-the-match display as Celtic played out an entertaining 2-2 draw with Atletico Madrid in the Champions League group stage on Wednesday.
Celtic are under no immediate pressure to sell O'Riley as the midfielder put pen to paper on a new four-year contract last month, keeping him tied to Parkhead until the summer of 2027.
However, speculation over a possible exit has been rife for some time, with the midfielder allegedly the subject of a rejected £10m offer from Leeds United in the summer.
TEAMtalk claims that Brentford are the latest club weighing up a January swoop for O'Riley, while the likes of Manchester United, Arsenal and Liverpool have all previously been credited with an interest.
Should any interested suitors step up their interest in O'Riley, journalist Fabrizio Romano claims that Celtic will demand that they pay a Scottish-record transfer fee for the midfielder.
The current record transfer fee in Scotland stands at the £25m that Celtic received from Arsenal for Kier
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