More than 2,000 pigs would be bred at the farm on the Moys Road and slurry spread on nearby land.
Thousands of people have objected claiming it would impact on their health and the environment.
However, an environmental statement said that the scale of the proposed development would have "no adverse impact" on either.
The BBC has tried to contact the farmer behind the plans, Thomas Simpson, but has not yet had a response.
Causeway Coast and Glens Council confirmed it has received more than 3,000 letters of objections.
"Over 3,000 letters of objection, five petitions with a total of almost 14,000 signatures and two letters of support have been received," said a council spokesperson.
"Once all consultations have been returned the application will be considered further - taking account of all material planning issues raised through letters and petitions of representation."
Thousands of objectors have also signed an online petition claiming the proposed farm would cause pollution and noise and affect traffic and rivers.
In February, the Public Health Agency and the Northern Ireland Environment Agency wrote to the council's planning department expressing their concerns.
"Our main concern remains the potential for bioaerosol releases from pig rearing activities and the associated anaerobic digester plant," said Gerry Waldron from the PHA.
A number of other government agencies - including NIEA, Shared Environment Services and Transport NI - also had concerns.
However, last month an environmental statement from an independent company concluded that the scale of the proposed development would have "no adverse impact" on people's health or the environment.
The report also stated that 500 more pigs would be included in the plans, bringing the total figure to more than 2,700.
It also stated that an anaerobic digester would no longer be needed and that slurry would be spread in local fields.
The council has said it is still considering the application.
Dozens of Limavady residents attended a meeting on Wednesday night to discuss their concerns.
Marcus Moore, chairman of Roe Angling Limited, said: "This is a disaster waiting to happen. I don't think the destruction of the environment is worth six jobs."
Former Justice Minister and Independent MLA Claire Sugden said further clarification was needed.
"We need to be sure that it isn't going to have a detrimental impact on the environment," she said.
However, the DUP's Adrian McQuillan said that the proposal would be good for the local economy and create a lot of jobs in the area.
The Ulster Farmers' Union said it did not discuss or comment on the development or proposed expansion plans of any farm business.

The 27-year-old right-back had just over 12 months left on his previous deal which he signed on arriving from Aston Villa for a reported initial £1m in June 2015.
He has appeared in 28 of Burnley's 30 league matches this season.
"I had a year left, but when the club and the manager approached me about a new deal it was a no-brainer," he said.

The decision was made after animal health investigators were unable to rule out the presence of H5N8 avian flu at a third farm in Wyre.
They said a "pro-active culling" would take place of birds including pheasants, partridges and ducks.
The Food Standards Agency said the disease was not a risk to food safety.
Public Health England said the risk to public health from the virus was very low.
The first outbreak was discovered last week at a farm in Wyre with 10,000 birds, followed by a second case involving a flock of about 1,000 birds.
Defra said the third premises would be cleansed and disinfected, "further reducing the risk that disease can be spread to other birds".
"Our investigations will continue and the restrictions already placed on the sites will remain in force until cleansing and disinfection is finished and the investigation is complete," a spokesperson said.
In January, there have been a number of other outbreaks of the virus, including at farms in Lincolnshire, North Yorkshire and in Carmarthenshire.
Campaigners opposed to plans for a controversial pig farm outside Limavady have met to voice their concerns.
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Burnley defender Matt Lowton has extended his contract at Turf Moor to the end of the 2019-20 season.
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About 63,000 birds are due to be culled at a Lancashire farm to prevent the spread of bird flu, which has already been found at two nearby premises.