NO!!! It is a superlative adjective.
e.g.
Dative ; close
Comparative ; closer
Superlattive ; closest .
The house along the road is close to our house.
The house , next but one, is closer to our house
The adjacent house is the closest to our house.
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No. Closest is a superlative adjective for "close." The adverb form is "most closely."