Sky said that Wal-Mart will bring in Sean Clarke, a former Asda director and the current head of Wal-Mart's Chinese operations.
The move would come as a major shock as Andy Clarke recently said that Dewsbury-born Roger Burnley is set to take on the top role. Mr Burnley is joining Asda as chief operating officer once he has completed a year's gardening leave from Sainsbury's in October.
It is not yet clear what impact such an appointment would have on Mr Burnley.
Sean Clarke, who is not related to Andy Clarke, started his career at Leeds-based Asda, where he served as commercial finance director.
He then worked as chief financial officer in Japan and Germany before moving to Wal-Mart Canada, where he led real estate and strategy.
He gained an MBA from Warwick Business School and a joint honours degree in mathematics and physics from Bristol University.
Asda has been suffering falling sales as shoppers switch to the discounters Aldi and Lidl, which are 10 per cent cheaper on average.
Wal-Mart International's chief executive Dave Cheesewright has said that the company is disappointed with Asda’s performance.
Sky said that Sean Clarke's appointment could be announced as early as this week.
Asda was unavailable for comment on Sunday.