The young centre-back is expected to complete his move to Hillsborough when the loan window opens on Saturday.
Oshilaja could play some part when the Owls take on Reading later that day.
The defender will boost a Wednesday backline that will be without defender Oguchi Onyewu (calf) at Reading.
Onyewu will be out for a few weeks, while Reda Johnson (hip) and Glenn Loovens (hamstring) both face fitness tests.
Defenders Martin Taylor (knee), Lewis Buxton and Kamil Zayatte (ankle) are also on the sidelines.