Oliver, who hasn't featured with the first-team since snapping his Achilles tendon back in October, could be given a month on loan at a League 2 or non-league club to help get him back up to speed.
The towering centre-half has featured in friendlies against Bradford (Park Avenue), Harrogate Town and Accrington Stanley in the last month or so, but Parkinson feels Oliver's return to full match sharpness will only happen with a regular supply of games under his belt.
Parkinson said: "The time is right in his recover to go out and play some games. We are just trying to find the right club for him.
"He has been making good progress but he can only go so far without a run of games.
"We are making calls and looking around for big Olly (Luke Oliver). Even though the transfer window shuts today (Monday), we can still get a club for him when the emergency loan market re-opens next week.
"It has to be the right club, of course, but Olly needs games now - there is not much more work he can do on the training ground alone."