The striker was overlooked by his country for selection for the Africa Cup of Nations next month, despite making himself available to be picked.
However, Clarke says that while the 31-year-old is sad to be missing out on the tournament, he is happy to be staying with the Baggies.
“Peter (Osaze) made himself available for Nigeria and they chose not to pick him,” said Clarke.
“He is obviously slightly disappointed that they have made that choice but he is delighted that he can stay and help us.
“I spoke to him and it is the choice of the Nigerian coach and he respects that choice. But he looks forward to helping us get a few more points instead of going away.”
Odemwingie has scored four goals for Albion so far this season.
Source - Punch news