According to The Sunday Times, Asda has already held talks with McLeod who is currently the chief executive of Asian retailer Dairy Farm International.
McLeod also has previous experience of leading Asda – forming part of the team that helped the grocer avoid bankruptcy before being sold to Walmart in a £6.7bn deal at the turn of the millennium.
He has also since gone on to lead bike and car parts retailer Halfords as well as Australian and US chains Coles and Winn Dixie.
The search for a new chief exec comes after Roger Burnley stepped down from his role as chief executive earlier this month.
While Burnley had been due to leave his post in 2022, the process has been accelerated “following completion of a transition period” under the group’s new ownership.
In turn, Asda revealed that the search for Burnley’s replacement is ongoing, with the supermarket chain’s shareholders set to make a further announcement regarding his long-term successor.
The group also claimed that “some additional appointments” will be made alongside its new CEO.