The Scottish Premiership side have become the latest team to register an interest in the exciting 20-year-old.
The League Two side are reportedly set to sell the 20-year-old at the end of the season, The Scottish Sun reports, but it appears that the Hoops may have to beat off some competition if they hope to be the ones to bag his signature.
Championship pair Birmingham City and Derby County both attempted to sign the Republic of Ireland under-21 international during the January transfer window (via The Scottish Sun), so may well be tempted to make another move for the youngster in a few months time.
It is hardly surprising that O'Dowda is attracting plenty of attention. The wide-man has scored seven goals in all competitions this term, including two in his last game which inspired Michael Appleton's side to a 3-0 victory over Barnet.
His form has been one of the key reasons why the U's find themselves in the automatic promotion spots in the division with just eight games to go.
The Scottish Sun suggests that O'Dowda would be seen as a replacement for James Forrest if he was to move to Parkhead. The Bhoys winger appears set for the exit in the summer, having turned down a new deal with the Scottish Premiership leaders earlier in the campaign (via Sky Sports).
While replacing Forrest with O'Dowda may not reap instant rewards, the potential that the Oxford starlet appears to have could mean that he proves to be a considerable upgrade on the inconsistent Scotland international.