The 21-year-old is attracting Championship attention after an excellent season.
The Championship side's manager Simon Grayson was present as the 21-year-old made his debut for the Republic of Ireland during their recent defeat to Belarus, The Irish Sun reports.
And while the youngster's promising performance was not enough to see him earn a place in the squad for this summer's European Championships, Grayson was clearly impressed as The Irish Sun claims that a bid could be imminent.
O'Dowda has enjoyed a fantastic season for the U's, scoring eight league goals and contributing three assists to help Michael Appleton's men secure automatic promotion to League One.
Understandably therefore, it appears that the Lilywhites are not the only club that look set to chase his signature in the coming months.
The Scottish Sun reported in March that the likes of Manchester United, Liverpool and Celtic are all monitoring the prospect's situation, so Preston may be relying on being able to offer first-team football to try and tempt O'Dowda to ignore any top flight offers and instead opt to move to Deepdale.