Daniel Farke’s side have already seen a bid for the Danish star knocked back by the Hoops in the ongoing transfer window.
Leeds are still keen on making room for a midfielder and could do business before the transfer window slams shut.
Celtic, however, are reluctant to lose O’Riley, who is a midfield cornerstone at the Scottish Premiership holders.
And it is now suggested that the Danish star is unlikely to leave Parkhead before the end of the transfer window.
O’Riley joined the Scottish giants last year from MK Dons on a four-year contract.
And Leeds are hoping that his inclusion in their squad will provide them with a midfield fillip moving forward.
Now with the Celtic star likely to stay put at Parkhead, it remains to be seen how Farke’s side will measure their transfer stance in the dying hours of the transfer window.