A Broxtowe Borough Council report has recommended shutting the building – which houses, among other things, an exhibition on the Eastwood during the time acclaimed author Lawrence lived there – to save money.
However, Malcolm Gray, chairman of the DH Lawrence Society, said it would be a “tragedy” if it closed.
He said: “If it closed and that link with Lawrence was severed it would be a great loss. It would affect tourism and the number of people coming into the town.
“As you drive into Eastwood, you have the signs directing you to the building. It’s an important part of the town. It would be disastrous.
The centre is housed in Durban House, Mansfield Road.
Built for The Barber Walker mining company in 1896, it is where Lawrence, as a child,used to collect his father’s mining wages.
Mr Gray said: “It’s a magnificent building and Lawrence talks about it as being a ‘fine’ building in his literature.
“It would be a tragedy if it was lost and a tragedy for the town if another link with Lawrence was gone.”
Mr Gray said it would also be a shame to lose the expertise of the staff who work there.
He said: “The staff are experienced on Lawrence and very helpful. They know a lot about the area and the links with Lawrence and that would be a great loss for the town.”
However, Mr Gray said he understood the council had to save money and the museum did not make a lot of revenue.
He said: “I agree there’s not a lot of money to be made out of Durban House.
“I don’t blame the council for that. They have decisions to make and priorities have to include care for the elderly and children.”
The DH Lawrence Society holds its meetings at the heritage centre and would be forced to find somewhere else if the building closed.
Mr Gray said they are considering looking into Greasley Beauvale School, where Lawrence studied, or Hall Park Academy.
He also said he would look at applying for a grant to open a new centre somewhere else, such as Eastwood Hall.
Mining historian David Amos, of Coach Drive, Eastwood, said the timing was “dreadful”, coming during the DH Lawrence Festival and just ahead of the 130th anniversary of his birth, today.
He said: “That’s the time when the centre brings people into the Eastwood area.
“You need some heritage in the area to pull people in.”
Mr Amos, who is on the festival’s steering committee, said he hoped there would be “alternative provision” if it closed.
A council spokesman said: “The council’s cabinet will consider a report on Tuesday, September 22, which recommends the closure of the DH Lawrence Heritage Centre building.
“The DH Lawrence Birthplace Museum is not affected by this proposal and the report will examine the future development of this nationally recognised museum.”
The museum was threatened with closure back inn 2010 but was saved by a grant from Nottingham University.