The 48-year-old ex-Oxford manager has guided the Cobblers to promotion from League Two this season, after a series of financial problems at the club.
Wilder is currently on a one-year rolling contract with the League Two side.
Jimmy Phillips has been in charge of Bolton since Neil Lennon left in March but could not prevent relegation.
Wanderers chairman Ken Anderson said on Monday that the club had a shortlist of three managers from applications they had received and hoped to make an appointment soon.
The Championship's bottom side have also confirmed that assistant manager Steve Walford and first-team coach Garry Parker have left the club.

Clive Weatherhogg's counsel told appeal judges that prosecutors now conceded there had been a miscarriage of justice over the coercion charge.
Appeal judges also agreed that a jury was misdirected over charges relating to the footage sent to relatives.
Mr Weatherhogg, 43, was jailed last May after being found guilty by a jury.
It is understood he will now be released from prison.
Sheriff George Way had remitted the case from Dundee Sheriff Court to the High Court in Edinburgh to be dealt with because of its greater sentencing powers.
Defence counsel Shelagh McCall QC told the Court of Criminal Appeal in Edinburgh that the Crown conceded there was insufficient evidence to prove lack of consent on the coercion charge.
The Lord Justice Clerk, Lady Dorrian, who heard the appeal with Lady Paton and Lord Turnbull, said: "We are satisfied the concession is well made."
Lord Turnbull said that information conveyed to the court seemed to show that even at an earlier preparatory marking stage in the case there were concerns over a lack of corroboration.
Lady Dorrian said the appeal judges were also satisfied that misdirections given to jurors by Sheriff Way over the charges relating to the footage sent to relatives were "material and constituted a miscarriage of justice".
Mr Weatherhogg, of Guthrie, near Forfar, Angus, had denied the charges during the trial, but admitted a separate charge of uploading the film to the internet.
He was jailed for four-and-years by Lady Wolffe with an additional 18 months for the charge he admitted.
The appeal hearing was told that Mr Weatherhogg had been in custody since March last year and had served the 18 month sentence, taking into account early release provisions.

Sam Sebastian, 18, also suffered a cardiac arrest at West Gate School, in Leicester, on 27 January 2016.
Eileen Coull, 63, from Leicester, and Marilyn Smith, 61, from Ratby, Leicestershire, will be sentenced at Leicester Crown Court on 13 July.
A charge of wilful neglect was dropped.
The teenager, who has mental and physical disabilities, slipped out of his rubber ring and was underwater for a minute and a half before being revived.
He also suffered lung damage following the swimming lesson.
The court had heard it was difficult to assess the extent of his injuries due to his disabilities.
Correction: An earlier version of this story stated Eileen Coull and Marilyn Smith were charged with wilful neglect.
Northampton's Chris Wilder is Bolton's preferred choice to be their next manager, BBC Radio Manchester reports.
[NEXT_CONCEPT]
A man jailed for six years for coercing a woman into having sex with a stranger and sending "revenge porn" to her family has had the convictions quashed.
[NEXT_CONCEPT]
Two staff members have admitted failing to take reasonable care of a disabled pupil who suffered brain damage when he was submerged in a swimming pool for 90 seconds.