Atalanta had a bid for Denmark through Celtic rejected last week.
Now, The Sun says Chelsea are in a position to enter the race.
New Chelsea manager Enzo Maresca is said to see O’Riley as an option for Conor Gallagher, who has seen an accepted offer from Atletico Madrid.
Celtic manager Brendan Rodgers has publicly suggested that O’Riley remain at the Hoops, despite the main interest that is emerging.