In response to a fan’s query about the status on his trials, the club tweeted: “Still training with the team, we will advise on any developments.”
The 21-year-old started training with the squad last Thursday coach Stuart Baxter is seeking to reinforce the centre of his defence.
Bukenya had been playing in Iraq up until the end of the 2012/13 season, but left Arbil FC, with who he won the domestic league in 2011/12, and is now a without a contract, meaning he can be signed outside of the transfer window.
He was also part of the Arbil side that finished as runners up in the 2012 Asian Football Confederation Cup competition, the secondary regional club competition behind the Asian Champions League.
His most recent national team appearance came for Uganda in a 3-0 friendly loss to Libya in June.
Bukenya would be the second Ugandan to feature for Chiefs after midfielder David Obua, who was a fan favourite with the AmaKhosi faithful during his time at the club.
Chiefs currently have three central defenders Erick Mathoho, Tefu Mashamaite and Morgan Gould, as well as untried teenager Lorenzo Gordinho.