Senior figures at the Kassam Stadium are understood to have been impressed by the former Arsenal and Wales midfielder despite his lack of managerial experience.
Ramsey, 35, retired from playing in April following a brief stint with Mexican club UNAM — the culmination of a career that also included spells at Juventus, Rangers, Nice and Cardiff City. He is currently studying for his UEFA Pro Licence through the Welsh Football Association, following a path taken by his former Arsenal teammate Mikel Arteta.
The Oxford Mail reports Ramsey had already held a previous meeting with the club's hierarchy and made a positive impression. A local journalist has since indicated there has been further movement. Ramsey drew two and lost one of three games as caretaker at Cardiff City in 2025.
Oxford are searching for a new head coach after parting ways with Matt Bloomfield following the club's relegation from the Championship. Bloomfield, who had replaced Gary Rowett in January, was unable to keep the club in the second tier.
Oxford will compete in League One next season and are hoping to make a swift appointment.