"There's been no approach to the football club [Newport], there has been an approach to myself," Edinburgh told a news conference on Thursday.
Such a move would appear strange from a Northampton perspective. Edinburgh and his board of directors turned down an approach from Portsmouth in December and his current side are currently just outside the play-off places.
Swapping that for a dogfight at the foot of the league would be an unlikely career move but Town have at this stage refused to comment and caretaker boss Andy King remains in charge for the game against Chesterfield on Saturday.
***Update*** The focus of Northampton's managerial hunt has switched to Chris Wilder of Oxford United according to reports on Friday.