It has been confirmed that Northampton have not made a formal approach to their League Two rivals for permission to speak to the 44-year-old.
However, the Exiles boss has said that representatives from the Cobblers have contacted him.
"There's been no approach to the football club but they're right in what they've said; there has been an approach to myself," Edinburgh told the South Wales Argus.
"But as I've always said I've got a job to finish here and I'm happy here. As with any individual that gets linked somewhere it's flattering but I've got a lot of work to do here.
"I'm ambitious, I want to be progressive and right now I feel I can do that here."
Edinburgh guided Newport to promotion from the Conference last season.