The 21-year-old playmaker broke into the West Brom side towards the end of the 1999/2000 season, scoring his only Baggies goal in the 4-4 draw with Bolton Wanderers at the tail-end of that campaign.
The highly-rated player survived a life-threatening kidney disease in 2001, but repeated knee injuries kept him out of contention for a place in Gary Megson's side during the recent promotion campaign.
In all Oliver played a total of 27 games for Albion, 23 of these from the substitute bench.
Club secretary John Evans confirmed that Oliver's career was on the brink.
"Adam's had a few serious knee injuries which may have concluded his career," Evans said.
"There is an element of insurance he will get from the PFA and from the club. It's very unfortunate especially as he is so young."
