Gallery director Chloe Geoghegan said the ''niche'' residency would give an emerging writer six weeks to produce about 5000 words.
The work would be motivated by the question: ''Is criticism still relevant?''
Miss Geoghegan said the successful applicant would be offered a space at the gallery in Dowling St and, if needed, off-site accommodation.
The fundraising had started so the resident writer could be paid a wage and she hoped to include unique Dunedin experiences during the residency.
The summer residency would be between January 19 and February 28 next year and would be an inaugural collaboration between the gallery and The Lumiere Reader, an online journal on arts review and film criticism.