The 23-year-old is attracting significant interest after enjoying a successful 2023-24 campaign, scoring 19 goals and providing 18 assists in 49 competitive appearances.
O'Riley netted 18 of those goals in the top flight to finish second in the Scottish Premiership's scoring charts, while his tally of 13 assists was more than any other player in the division.
The Denmark international helped Celtic retain their league title and their Scottish Cup crown as well as being named the club's Player of the Year.
As a result of his impressive performances, O'Riley has emerged as a transfer target for Europa League winners Atalanta.
Celtic turn down third Atalanta offer
The Serie A club saw their first two offers knocked back by Celtic, before they returned to the negotiating table with a third bid.
However, according to Gianluca DiMarzio, Celtic have now rejected Atalanta's third offer of €17m (£14.4m) for O'Riley.
The Scottish champions will feel they are in a strong negotiating position, with O'Riley under contract under the summer of 2027.
Atalanta must now decide whether they want to submit an improved proposal or turn their focus to alternative targets.
Who else is interested in O'Riley?
Even if Atalanta decide against making a fourth offer, there is a possibility that O'Riley could still leave Celtic this summer.
The midfielder has been linked with Juventus, Roma and Atletico Madrid, while Southampton are believed to be considering a move as they look to strengthen their squad ahead of the Premier League season.
Celtic boss Brendan Rodgers admitted he is "fairly relaxed" over O'Riley's future, recognising there is always a risk that players could depart to compete in some of Europe's major leagues.
While there is uncertainty surrounding his future, O'Riley has been involved in the first two matches of Celtic's pre-season tour of the USA.
The former MK Dons man scored a brace in a 2-0 win over DC United, before he provided an assist in Tuesday's 4-3 victory over Manchester City.
Khimki 
Lokomotiv Moscow 
Crvena Zvezda 
Benfica 
Feyenoord 
Bayer Leverkusen 
Spartak Moscow 
Krylya Sovetov 
Atalanta 
Arsenal 
Atletico Madrid 
RB Leipzig 
Monaco 
Barcelona 
Bordeaux 
Quevilly 
Pec Zwolle 
AZ Alkmaar 
Alaves 
Sevilla 
West Ham 
Chelsea 
Sampdoria 
Sudtirol 
Werder Bremen 
Bayern Munich 
Leicester 
Everton 
Liverpool 
Bournemouth 
Tottenham 
Brentford 
Dynamo Kyiv 
Rukh Lviv 
Juventus 
Napoli 
Rubin 
CSKA Moscow 
Voltigeurs De Chateaubriant 
Crystal Palace 
Manchester Utd 
Eintracht Frankfurt 
Borussia Monchengladbach 
Rangers 
Dundee 
Valencia 
Girona 
Vitoria Guimaraes 
FC Porto 
Rodez 
Go Ahead Eagles 
Ajax 
Reims 
Paris Saint Germain 
Real Madrid 
Espanyol 
Fiorentina 
Lazio