Obua is available from South African giants Kaizer Chiefs and is understood to have trained with the Hammers on Friday in a bid to impress Alan Curbishley.
Obua recently told reporters: "As a professional, I have to weigh up my options and make a decision. I have many offers, but I'm not about to rush.
"One thing is for sure, I'm not returning to South Africa. I have nothing to prove in South Africa because I believe I've won everything as an individual. I need a new challenge that will only be realised in Europe."
Obua has won over 20 caps for Uganda, even scoring a hat-trick for the Cranes in an African Nations Cup qualifier against Niger in September 2007.