Blackhurst was in the running for the top job at Asda, but lost out to current boss Andy Clarke, prompting his departure last year.
Matalan is currently without a permanent chief executive after Alistair McGeorge left in September last year.
The discount retailer's finance director Paul Gilbert has been in the role of acting chief executive in the interim.
Blackhurst started his career at Tesco in 1988 and spent 18 years with the supermarket, during which time he held various buying and commercial roles.
He moved to rival Asda in 2006 to become food trading director, and played a key role in reinvigorating the supermarket chain's business.
Blackhurst is expected to be announced as chief executive of the private company next month.
Matalan was unavailable for comment.