By Toby Prince
The 29-year-old is available on a free after his contract with German side, Schalke 04, ran out in the summer.
However, the former Lyn Oslo striker had been sidelined with long-term injury and has only just returned to fitness.
Sunderland are short of goals and Black Cats boss, Sam Allardyce, hopes Obasi can help should he prove his fitness over the next two weeks.
“There’s a trial-list in at the moment. He used to play for Schalke but he’s been injured,” Allardyce said of the forward.
“He’s a Nigerian international and we are just seeing because he’s got a reasonably good CV, in terms of where he’s played before.
“He has been fraught with a bad injury, which is why he’s not been fixed up with a club yet, but we’d like to see him for this week and perhaps next week.
“But I need someone who has an impact now, not in three weeks time, so it will be a difficult task I think. But he’s here and if he can show us anything we haven’t got then there maybe something we can do.”
In his three years with Schalke, Obasi scored just four goals in 34 games in all competitions.
He has been capped 18 times by the Super Eagles with four goals.