Charles Heintzelmann, with Milestone Ventures of Indianapolis, said his company has an option to buy several acres of undeveloped land located between South and Martinsville streets.
He had hoped to present his plans for the two-story, 31-unit complex to the Board of Zoning Appeals Tuesday night but there were not enough members present to vote, so the meeting was postponed until next Tuesday at 6 p.m.
Heintzelmann is asking for a special exception to the city's zoning ordinance to allow for a multi-family dwelling in a single-family district.
The company has built similar complexes in communities the size of Greencastle and smaller, including Linton, Rising Sun, Morengo, Corydon, Salem and Orleans.
Monthly rents for the units range from $220 to $515 per month for a one-bedroom and $300 to $665 for a three-bedroom.
Heintzelmann said the company plans to start out by building 31 units and possibly double that number in the future.
The apartments will be available for low-income residents, however, they are not what the public commonly knows as "government subsidized housing."
Heintzelmann explained that his company does receive tax credits from the federal government, which it uses to construct the apartments. In turn, it must offer a certain number of the apartments at lower rental rates so that low-income families can afford them.
Several residents attended Tuesday night's meeting but did express concern about the tenants. They were concerned about drainage, road traffic and buffering between the existing residential area.
Heintzelmann will return next week to make his formal request to the BZA. The meeting will begin at 6 p.m. Tuesday at city hall.