HITC Sport understands that the Cobblers boss is in the frame to succeed Dean Saunders at the Proact Stadium.
The Spireites are in the market for a new boss after parting with the services of Dean Saunders.
He has been relieved of his duties with the club on a sorry run of form that has delivered four straight defeats and dropped them to 16th in the League One standings.
A new direction is being sought, and numerous candidates are being considered.
HITC Sport reported earlier in the week that Forest Green Rovers boss Adrian Pennock is in the running, along with the likes of Danny Wilson and former players Jack Lester and Richie Humphreys.
Wilder is another of the leading contenders, and would come highly rated.
He is regarded as one of the best young managers in the country after guiding Oxford back into the Football League from the Conference and consolidating them in League Two before taking over at Northampton in January 2014.
Wilder helped to keep Northampton up against all the odds in his first season in charge – after taking over with the side in the relegation zone.
Wilder could consider his future at Northampton due to the club’s financial problems, with the Cobblers handed a winding-up petition by HM Revenue and Customs (HMRC) earlier this month due to the £10.25m loan the club owes the local council.