If the owner is directly responsible for the area being audited, i.e. he/she is the supervising authority or performs the function himself/herslef, he may not be the auditor.
The standard reads ".... shall be carried out by personnel independent of those having direct responsibility for the activity being audited".
In short, the auditor may not be directly responsibly for the area or task being audited.
I would recommend an outside auditor conduct the internal audits or that the owner train others in his/her organization to be internal auditors.