HITC Sport understands several Premier League clubs have already been knocked back in trial requests for the talented winger.
The talented winger has come through the ranks at the Kassam Stadium, but dozens of scouts from the Premier League and Championship have been flocking to take in his displays and many believe him to be the best young player in League Two.
The 20-year-old made his debut in 2013 but has become a first-team regular under Michael Appleton, who has been fielding call after call about his young forward.
O’Dowda, an Irish Under-21 international, is now high on the agenda of a host of top clubs and Oxford have rebuffed a number of requests to take him on trial.
HITC Sport has learned that Liverpool are heading the chase and are one of those who have failed with requests to let him train with the club, whilst city rivals Everton, Manchester United and Tottenham Hotspur are also keen.
Liverpool have a tremendous record of plucking young wingers from the Football League in recent years, highlighted by the emergence of the likes of Raheem Sterling and Jordon Ibe, both of whom were taken to Merseyside from the lower leagues.