Al Nasr had asked West Brom to inform them what they considered to be an acceptable fee by Tuesday, after their initial bid of £850,000 was rejected.
But that deadline has now passed without further communication from The Hawthorns, leaving 'The Blue Wave' to look elsewhere for summer recruits.
Nigeria striker Odemwingie, who has one year left on his contract, continues to train with the reserves having been told he does not feature in manager Steve Clarke's plans for next season.
Odemwingie has scored 31 goals in 90 appearances for the West Midlands club since joining from Lokomotiv Moscow in August 2010.
But he fell out of favour last season after agitating for a move to QPR that failed to materialise.