Mileage between your home and your office (commuting miles) are not deductible. However, if you work at more than one location during the day, you can claim the miles for getting from one place to another. So if you go in to your office in the morning, and then go to 3 other locations during the day in the course of your job, you can deduct the mileage from your office to those 3 other locations.
If this has been helpful, please press the "accept" button. Positive feedback is also greatly appreciated. Thanks for the question and have a great day.
Sorry I misunderstood your question. No, your employer is not required to reimburse you for mileage for business use of your own vehicle. But if he does not, then you can claim those expenses as a deduction on your taxes. I hope this answers your question, but if not, let me know.