O’Nien is one of four players Sunderland have offered a new deal, with the ex-Wycombe man soon-to-be-out-of-contract this summer.
Charlie Wyke, Aiden McGeady and Denver Hume have also been offered new terms.
Preston had been credited with a strong interest in O’Nien this week, however, that has been played down.
Lancashire Live report: “Other Championship sides have been linked with him and while PNE did express an interest, they did not choose to pursue a move.”