By Toby Prince
Obasi, who is a free agent after being released by German Bundesliga side, Schalke O4 in the summer of 2015, has been on trial with the Black Cats but was unable to convince coach Sam Allardyce for a deal.
The 29-year-old has been plagued by injuries over the last one year and is yet to fully recover.
He endured a miserable time at Schalke after making just 10 Bundesliga starts in three years, an awful stat for a player once considered the hottest property in Germany, while at TSG Hoffenheim.
Allardyce has been considering options on the Bosman market since taking charge at the Stadium of Light a fortnight ago, with one place available in his squad to bring in a free agent before the transfer window re-opens in January.
Daily Mail now reports that the Nigerian is now exploring other options after his proposed move to the Premier League side stalled.