Brighton only signed the 24-year-old last year from Scottish champions Celtic, and although he was a major acquisition, he has struggled to find a regular place in the Seagulls' side this season.
Now, a report in the football media gossip columns says that his manager, Fabian Hurzeler, will let him leave the South Coast if a suitable price is agreed.
Everton boss David Moyes is claimed to be a strong admirer of the player and allegedly wants to move for him as part of his squad rebuild this summer.
Previous stories have linked the Blues with O'Riley, and now the field could be clear for Moyes to put in a bid for a young and obviously talented footballer who presumably is willing to consider moving on.
O'Riley has played across the midfield and seems best suited to a more deeper-lying position where he can use his ability to pass and create.
He would not be a like-for-like replacement for Idrissa Gueye, and Carlos Alcaraz will probably be taking over Abdoulaye Doucoure's role, so it is not exactly clear what O'Riley's place would be.
And as has been mentioned before, adding further reinforcements in the engine room might not seem to be the Toffees' main priority, with other areas of the team needing more attention.
Clearly, Everton need additions in attack most of all, with a new striker an absolute must, especially if Dominic Calvert-Lewin leaves on a free and Beto is sold, which it is rumoured he might be.
But with Doucoure gone and Gueye still to sign a new contract—even though he seems likely to do so—the Blues could use more options in the middle.
A deal for O'Riley still looks a long shot, and it is probable that other alleged midfield targets are more likely to be on the cards, but a bid of around £25 million could enable the Toffees to get their man.