Former Nigerian international
Obasi has been searching for a club since he was released by Bundesliga side Schalke 04 and has had trials with the likes of Sunderland, EintrachtFrankfurt and German RegionalligaWest side SVWaldhof.
Speaking about the move, the former Super Eagles forward says the move is a great chance for him to come back.
“I’m injury free, but need some time to get in shape. I will do my best for Lillestrom,” he told Nrk.no.
According to Norwegian website Nrk.no, coach of Lillestrom, Runar Kristinsson is looking to sign Ogbuke to replace their first choice striker, another Nigerian, Frederic Friday who is certain to leave.
Ogbuke scored a brace in a Lillestrom test game 2-3 defeat to Valerenga and kristinsson hopes he will be able to conclude the signing.
"I hope to sign him but we will sit down with him the next few days but finally, it is up to the board," Kristinsson told the website.
"He has shown good form and he wants to get out there again.
"He has experience at a high level, and he brings experience to the younger boys. He is a true professional and a role model."