LivingSocial, the fast-growing daily deals company that has become one of the biggest private employers in the District, would make the city its long-term home under a deal proposed by Mayor Vincent C. Gray (D).

The city’s plan arrives as the five-year-old company has been wooed by jurisdictions nearby and outside the area eager to poach the juggernaut and its prize 956-person D.C. payroll. The company adds dozens of new hires every month.

Gray is willing to rewrite tech incentives that would save LivingSocial up to $32.5 million in taxes over a five-year period beginning in 2015. By then the company, which has yet to turn a profit, expects to be operating in the black and to have hired an additional 1,000 people in the city. To maximize its savings, at least half of the new hires would be required to live in the District or move to the city within six months of being hired.

Begun over beers by 20-something entrepreneurs at a D.C. bar, LivingSocial has become one of the higher-profile area technology companies to come along since AOL, whose ascent minted dozens of millionaires and put entrepreneurs Steve Case and Ted Leonsis on the map.

LivingSocial’s growth potential — it is diversifying into new businesses, including a high-tech local clubhouse for live events — could help transform the District into a hot destination for software engineers and other young techies looking to latch onto the boom in online businesses.

The company, which has hired bankers to take it public, already has made its economic presence felt in the region through everything from hotel rooms to the local bike-sharing program to taxi cabs and restaurants. From conferences to Christmas parties to recruitment, the company is spending tens of millions in the local economy.

Gray, who wants to keep the tax dollars flowing, issued a statement saying he envisions LivingSocial serving as the hub of the city’s growing tech sector. By keeping the company here, he expects the city to earn $133 million over a 10-year period in taxes on corporate income, personal income, hotel stays and other LivingSocial spending.

“LivingSocial is a very large part of the reason why other tech companies of all shapes and sizes have flocked to the District,” Gray said. “We want to see that trend continue, and it was important to us to make sure they stayed and expanded in the very place they began, the District of Columbia.”

LivingSocial co-founder and chief executive Tim O’Shaughnessy said in an interview he has been considering how to address the company’s growing costs. O’Shaughnessy, 30, the son-in-law of Washington Post Co. chairman Donald E. Graham, said that Washington was “part of LivingSocial’s DNA.”

“We started here and we are a local business and we have worked with a lot of the local businesses around here. We have a lot of people who moved to D.C. or went to school here and they stayed because LivingSocial was an interesting place to work at,” he said.

O’Shaughnessy said he stressed in meetings with Gray, however, that it would be more expensive to grow in Washington than elsewhere.

“We’ll make a commitment to the District if the District will make a commitment to us,” he said.

Both sides are eager to make it work, but the deal requires passage by the D.C. Council. LivingSocial could still look elsewhere, and Gray said it would be “devastating” if the company were to leave.

Although LivingSocial’s value is estimated at around $4 billion, the company has yet to turn a profit, and some question whether the daily deals space has long-term potential. In February, Amazon, which owns almost one-third of the company, revealed in a regulatory filing that LivingSocial lost $558 million in 2011. LivingSocial’s revenue was $245 million.

But its growth has been remarkable. LivingSocial has sold more than 63 million vouchers since it began and now has more than 60 million members worldwide in 647 markets across 25 countries. The company has nearly 5,000 employees worldwide. Besides Amazon, its stakeholders include O’Shaughnessy and his fellow founders; Tysons Corner-based Grotech Ventures; and Steve Case’s Revolution group of investment funds, headquartered in the District.

“Look at what we’re doing for the city and the employee growth, the payroll growth,” O’Shaughnessy said. “And this industry, it’s clearly young, but it’s proven to be pretty viable, and we are one of the market leaders in that space, so it’s an investment in us, and it would also be an investment in the city.”

One of the company’s growing costs in the District is real estate, where it has five offices along Seventh Street NW and a headquarters at 1445 New York Ave. NW, near the White House. It has been looking to buy or lease a much larger building, 350,000 square feet or more, where it could consolidate its growing District workforce. A company spokesman said a final decision on where to locate had not been made.