Ameobi joined Wanderers in October and made his debut the following day, scoring in a 1-1 draw against Leeds United at Macron Stadium.
The 34-year-old has since gone on to make eight appearances for the Trotters, but has made just one substitute appearance since coming off injured during a defeat at Hull City on December 12.
Standing in during the absence of Neil Lennon, Bolton assistant manager Steve Walford revealed Ameobi is in contention for selection against Eastleigh on Tuesday but also confirmed the former Newcastle United forward would be able to sign for another club from next week.
"Shola is fine, he's fit," Walford told The Bolton News. "But he's obviously on a short-term contract which runs out on Saturday and we're not in a position to renew anyone's contract, so this will be his last week at the football club.
"He's done fine in training and he's ready to play tomorrow if need be.
"You'd like to keep someone of his experience around the football club but we're not in a position to do that. It's a shame but I'm sure he'll get fixed up somewhere else."