What does that water heater mfr. say? If it calls for a non-combustible base, then write it up. Regardless, the base must be capable of supporting the load. Figure a 40 gallon water heater full of water weighs about 400 lbs. If that water heater is sitting on 4 square feet of conventional construction rated at 40 lbs per sq. foot, then it is inadequate for the load.
Then again, with a closet, do you have your circumferential clearance required by the WH mfr? Gas or electric? Need MUA and combustion air?
What is the construction under the WH?
Any pics?

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Keep the fire in the fireplace.