Kettering Town chairman Imraan Ladak has called for a public meeting with the local council to discuss the Poppies' future at Rockingham Road.
Kettering's lease runs out in three years - and is unlikely to be renewed.
But Ladak has called for a public meeting with the council, suggesting: "I want to meet them and ask questions but I want to do it publicly."
"If they care about the club then they will have no problem having a meeting," he told BBC Radio Northampton.
"If they have nothing to hide, I would like to meet them at our social club on any day or any evening in the next two weeks."
But Kettering Borough Council leader Jim Hakewill wants to meet the club privately.
"We wrote, over three weeks ago, asking Kettering to please come in with their plans," Hakewill told BBC Radio Northampton. "And we wrote last week to see if they got the letter and that the door is open.
"The only way we can progress is with a proper business meeting with the parties concerned, so we are waiting for Imraan's response."
Poppies fanzine editor Peter Short is concerned with the developments.
"The chairman has tried and tried and tried again to find a ground solution for Kettering," Short told BBC Radio Northampton. "But one hasn't appeared yet.
"The chairman keeps alluding to not having a football club in the borough so that doesn't necessarily mean that Kettering Town won't exist.
"It could mean Kettering ground-sharing or moving out of the borough which could mean a move to Rothwell, or Corby, or Desborough or dare I say it Rushden and Diamonds?"
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