Caerleon-born Machen, who died in 1947, is known for his story The Bowmen, set in World War One, which gave rise to the legend of the Angels of Mons.
Newport council is consulting on budget plans that could see the library shut.
A spokesman said it would relocate the reference library if the building shut but no decisions have been made.
The Friends of Arthur Machen literary society said its members, who include comedian Stewart Lee, actor Barry Humphries and writer Alan Moore, are writing to the local authority.
Friends' founding member Godrey Brangham said: "This obviously is of great concern regarding the Machen collection in the reference library."
Friends' chairman Ray Russell said: "Newport holds the finest public Machen collection in the UK.
"We'd like them to preserve it, develop it, and keep access to it open.
"Arthur Machen was a local son of Gwent who won worldwide literary fame, and it is hoped that Newport will continue to honour his work."
Arthur Machen 1863-1947
•Born 150 years ago in Caerleon, south Wales
•Fantasy and horror writer
•Works include early self-published book Eleusina, The Great God Pan and The Three Imposters
•Fans include Stephen King, Mick Jagger and Rowan Williams
•His portrait is in the National Museum Wales
More about the first modern horror writer
The leader of the council has met with the group, and a spokesman said: "If the proposal to close the central library building did go ahead then the council would consider where the best possible place to relocate the reference library would be."
The consultation on the council's budget savings proposals continues until 16 January 2015.

14 February 2017 Last updated at 08:20 GMT
It's part of a celebration of the re-opening of the Settle to Carlisle line in Cumbria which had to be closed after landslides damaged the railway line.
Tornado, the steam train pictured above, will run two return journeys a day between parts of Cumbria and Yorkshire from the 14 to the 16 of February.
The company which owns the trains think they will be pretty popular!

Last month, the 32-year-old left League Two side Luton Town by mutual consent to return home.
But the ex-Derry City winger said when his wife, Laura, was diagnosed, everything paled into insignificance.
"I called Michael (O'Neill), explained what had happened and told him I wasn't going to be available for the Euros," he said.
"When something like that happens, your only thought is for your family."
McCourt told the Times that his wife was returning home from a holiday when their life was turned upside down.
"The flight landed at Gatwick and was taxiing to the airport when she had a seizure on the bus," McCourt said.
"Paramedics were called to the scene and they rang me.
"They said they were going to send her to East Surrey Hospital. Naturally, I was very concerned.
"Within 48 hours it came back that they had found a brain tumour," he said.
The doctors told the couple they needed to operate on the tumour and remove it as soon as possible.
Although the tumour was benign, it was growing. The date for the operation was 9 June, the day before Euro 2016 started.
McCourt said Northern Ireland boss Michael O'Neill told him to be there for his wife and 'don't even think about Euros'.
"Laura didn't need the attention it would have created if he had said what was really happening," he adds.
The operation was successful and Laura has now been given a positive diagnosis.
"It was absolutely nerve racking," he said, "but thankfully we were given the best possible news afterwards, which was that everything had been positive.
"Laura is now recovering and we're told that in four to six months, please God, she will be completely back to normal."
Fans of horror writer Arthur Machen have called on Newport council to protect the collection of his books and papers at the city's central library.
[NEXT_CONCEPT]
For the first time in more than 50 years a steam train will be running a regular service in England, but only for three days.
[NEXT_CONCEPT]
Ex-Celtic footballer Paddy McCourt has told of his wife's diagnosis with a brain tumour.