Wilder left last week for Sheffield United, having guided the Cobblers to the League Two title this season.
Former Wales international Page, 41, has been in charge of Vale since October 2014 and led them to a 12th-placed finish in League One this term.
Page has a year left on his contract at Vale Park so compensation is due.
The ex-Watford and Sheffield United defender has been in the Potteries for five years, having first been brought in to join the Vale coaching staff in 2011 by predecessor Micky Adams.
Page took caretaker charge following Adams' resignation in September 2014 and was given the job on a full-time basis a month later, helping them avoid relegation and finish 18th in 2014-15 before a mid-table finish this campaign.
He had been linked with both the Cardiff and Sheffield United jobs, but is set to join a club which won the fourth tier by 13 points last season under Wilder.
That came in a season which included takeover uncertainty, a £10.25m loan repayment to the local Borough Council and a winding-up petition from HM Revenue & Customs.
Kelvin Thomas' November takeover of the Cobblers resolved those fears and they ended the season on a 24-match unbeaten run.
Northampton Town are set to appoint Port Vale boss Rob Page as manager to replace Chris Wilder, reports BBC Radio Stoke and BBC Radio Northampton.