The building, which used to be part of a pig farm that stopped trading in 2003, is located to the east of the village and north of Cowesfield Green.
It is owned by the occupiers of nearby Cowesfield House.
Drawings submitted with the plans show that each of the one-storey dwellings would have three bedrooms, a lounge, kitchen and dining area, a bathroom and a utility and storage room.
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A statement submitted by Atlas Planning on the applicant’s behalf says: “The proposal will introduce five new dwellings to the area, providing more choice for house buyers and helping to achieve housing targets in Wiltshire Council, whose housing supply is lacking.
“In the short term, the conversion of the building will provide employment benefits for the construction industry, which is a clear economic benefit of the scheme.
“Another longer-term economic benefit of the proposed change of use is the boost to the local economy which will come from new residents utilising local services.
“The new dwellings have been designed to complement the existing agricultural form of the building and owing to its discrete position on the site, would not harm the character and appearance of the area.
“The site has suitable access and is large enough to provide suitable amenity space for occupiers and high-quality accommodation.”
A structural report says the barn’s steel frame is “well constructed and has only minor defects” which can be easily repairs and “should not affect future plans for the building”.
The construction site and homes would be accessed via Romsey Road.