The Walks does not meet the standard required by the Football Conference
King's Lynn will receive all the support they need from the local council as they appeal the Football Conference's decision to demote them.
The club were told on Wednesday they face relegation because The Walks does not meet ground grading standards.
Ray Harding, chief executive of King's Lynn Borough Council, told BBC Radio Norfolk the club has their support.
"We'll help them all we can with the appeal, the last thing we want is to see the club relegated," he said.
The club and the council, who own The Walks stadium, say they have sent written assurance to the League that improvement works will be completed in time for next season.
"We agreed that we'd take on upgrading the floodlighting, increasing the size of the changing rooms and providing additional changing rooms and medical facilities.
"A substantial investment from the council, at a difficult economic time, of around a quarter of a million pounds.
"We've written and confirmed to the Conference that we'll carry out that work during the close season, it's a real shame if they think that's not an adequate response," he said.
We're helping as much as we can on the physical side of the buildings, and the club have been doing great works on the pitch
King's Lynn Borough Council chief executive Ray Harding
The club were given 14 days to submit their appeal, and Harding says the council have always seen the Linnets' status as important to the rest of the town.
"It's important to the image, and the feel-good factor of King's Lynn if the club's advancing up the leagues, which it has been in recent years.
"We've helped in the past, with a previous investment of about £200,000, to upgrade the fabric of the stand itself.
"We're helping as much as we can on the physical side of the buildings, and the club have been doing great works on the pitch," he added.
King's Lynn recently secured safety after the club's first ever season in non-league's second tier.
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