Wild, 38, has been long-admired by the Spireites board and was a contender for the manager’s job before Rowe was appointed in November 2020.
Wild has led the Shaymen to third in the National League this season, one place below the Blues on goal difference, despite working with a limited budget compared to many of the teams at the top of the division.
The former Oldham Athletic boss has been consistently linked with managerial vacancies at clubs in the Football League including Hartlepool United and Rochdale last year.
Wild, who has been at Halifax since 2019, has a strong reputation for player recruitment and a number of his signings have been poached by bigger clubs in higher leagues.
His Halifax team impressed everyone with their attractive style of play when they drew 1-1 at the Technique Stadium in December.
Financially the deal will not be a problem but the big question mark will be whether Wild wants to stay loyal to the Shaymen and potentially lead them to promotion.
Earlier in the week a deal to bring Paul Cook back to the Spireites broke down after an agreement could not be reached.
First-team coach Danny Webb will be in charge again on Saturday when Dagenham and Redbridge visit the Technique Stadium.
After Dagenham, Town have a top-of-the-table clash away at Stockport County to look forward to.
Meanwhile, Halifax are at home to fellow promotion rivals Bromley this weekend.