The owner of a Greenwich office property with waterfall views has proposed converting some of the space to apartments, subject to approval from town regulators.

Most recently serving as the temporary Greenwich headquarters of L Catterton, The Mill offices at 10 Glenview St. have been largely unoccupied since the private equity investment firm moved to new offices on West Putnam Avenue.

The Mill has been offering space at between $39 and $42 a square foot, according to the most recent property listing posted on the Loopnet commercial real estate website, in line with average asking rents outside the town’s central business district.

In a request filed this month with the Greenwich Historic District Commission, the building’s owners proposed converting the majority of space in two of the property’s buildings into apartments, along with the ground floor of a third. Units would be offered at market rates, according to the commission, with upscale apartments in that section of Greenwich priced between $2,600 and $5,000 a month on the website.

The Mill’s history dates back to a late 18th-century textile mill along the Byram River, in what was then the town of Sherwood Bridge and a centerpiece of Greenwich’s Glenville district today.

The project would include the historic “1881 building” that, with a clock tower overlooking the waterfall, is the most visually striking of the complex that includes multiple structures.

If relatively distant from the town’s main train station, the Mill has played up its relative proximity to Westchester County Airport, the Merritt Parkway and a small mix of Glenville restaurants and retailers — and most of all, its location on a leafy glade overlooking the waterfall.

But with companies looking to increase their appeal to millennials as a place of employment, many businesses have been looking for space in downtown areas and near rail stations offering easier access to New York City.

Whereas downtown Greenwich had a 13 percent vacancy rate as of the second quarter, the town’s office parks outside the central district were closer to 23 percent vacant as estimated by the Stamford office of Cushman & Wakefield.

Includes prior reporting by Kaitlyn Krasselt.; 203-842-2545; @casoulman