The Baggies' boss insists he has the resources to continue his side's superb start to season even if some of his players feature in the tournament in South Africa in January
The Baggies have made a magnificent start to the Premier League season sitting in sixth place having lost just one game in seven.
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However, the loss of two regulars in Mulumbu and Odewingie, to DR Congo and Nigeria respectively, will be taken care of by Clarke and his squad.
"As things stand, we're comfortable with the squad we've got," he told reporters.
"If not, it's a good month for it because the transfer window is open again in January, and if you need to address the situation you can."
Odemwingie has 54 caps for Nigeria while Mulumbu, who has twice made himself unavailable for his national team, could add to his 12 international caps in South Africa.