Ashton joined the Third Division club on a initial month's loan from Leicester at the start of the season and Atkins wants to tie him down a two-year deal after impressing at The Kassam Stadium.
Atkins fears he might lose the 20-year-old if he cannot agree a deal quickly.
"It's out of my hands," Atkins told the Oxford Mail.
"But the lad wants to come here, Leicester are prepared to let him come on a free transfer and he's not on massive wages there, so it shouldn't be a problem.
"Hopefully something can be sorted out soon, because if he's not here on Monday he'll be at another football club."
