Ex-Huddersfield Town and Portsmouth manager made early favourite to land job with Barnsley's League One rivals
The U’s are just three points adrift of the summit in League One but have lost boss Liam Manning to Championship side Bristol City.
They are now in need of a new head coach, with time potentially of the essence if they are to avoid losing momentum.
Cowley has been out of work since leaving Oxford’s third tier rivals Portsmouth earlier this year.
Prior to his Fratton Park stint, he was in charge of Championship strugglers Huddersfield Town.
He has been linked with a range of vacancies since his Portsmouth exit but has yet to make a return to the dugout.
BonusCodeBets have priced Cowley at 2/1 to take the reins.
There has been a spate of managerial changes in the EFL recently, with Oxford the latest club to begin the hunt for a new boss.