If the space you are claiming as a home office meets the home office qualifications (exclusive use/regular use/principal place of business) and it is part of the space that you are paying rent to use, then you can claim the home office deduction.
You would use the simplified method or the actual expenses method, but either way, you would indicate that you 'rent' your home and do not own it. You would not be depreciating the part of the house that contains your office since you do not own the house.
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