How to mock a third-party class in private static method?

Here's the code:

public final class APIClient {
    private static Identity identity = createIdentity();

    private static Identity createIdentity() {
        CredentialsProvider provider = new CredentialsProvider(API_USER);
        Credentials creds = provider.getCredentials();

        identity = new Identity();
        identity.setAttribute(Identity.ACCESS_KEY, creds.getAccessKeyId());
        identity.setAttribute(Identity.SECRET_KEY, creds.getSecretKey());

        return identity;
    }

}

How can I mock a CredentialsProvider when unit test:

@Test
public void testCreateAPIClient() {
    // mock a CredentialsProvider
    client = new APIClient();
    Assert.assertNotNull(client);
}

Thanks in advance!