The board of Frasers Group, which also owns House of Fraser, said talks were under way for Michael Murray, 31, to succeed the billionaire on 1 May 2022.
Mr Murray is the son of Doncaster property and business magnate Mick Murray, who set up the all-conquering Doncaster-based Lazarus Properties with business partner Lloyd Nicholson in 1997.
The firm is one of the town's best known and owns prime residential and commerical buildings across the region as well as London.
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The move would see Mr Ashley step down from as chief executive but remain on the board as an executive director.
Mr Ashley founded Sports Direct in 1982 and retains 64% of the group.
Mr Murray, engaged to be married to Mr Ashley's daughter Anna, is currently "head of elevation" at Frasers and is in charge of modernising stores and transforming the business.
Murray met Anna on holiday in Majorca in 2011 and the couple now live together in a £10.7 million mansion in Belgravia.
In stock market statement, Frasers Group said it was "currently proposed" that Mr Murray would assume the role of chief executive, with a "reward and remuneration package" now being considered.
"The board consider it appropriate that Michael leads us forward on this increasingly successful elevation journey," Fraser's Group said.
Mr Ashley has become one of the biggest figures in the High Street in recent years, snapping up a number of troubled British brands including House of Fraser, Evans Cycles, Jack Wills and Game.
The group is now worth around £3bn and operates almost 1,000 shops.
Frasers Group revealed the leadership change in its latest full-year trading figures on Thursday, in which it said its revenue fell 8.4% to £3.6bn from £3.9bn in 2020.
Its sports retail revenue also decreased by 10.7% from £2.2bn to £1.9bn due store closures caused by the Covid-19 pandemic, the company said.
Pre-tax profits also dived by 94.1% to £8.5m for the year to 25 April, compared with £143.5m in the previous year.
In a statement Mr Ashley said: "Our stores in the UK have reopened above expectations and our online channel continues to significantly outperform pre-Covid-19 periods.
"None the less, management remains of the view that there is a high risk of future Covid-19 pandemic restrictions, likely to be over this winter and maybe beyond."
Who is Michael Murray?
He was educated at the private Sedbergh School - which counts former England rugby captain Will Carling among its former pupils.
He set up an events company with pal Toby Mullins, 26, after they were students at Reading University. Their club nights, where tickets cost £5 and revellers down cheap booze have proved popular in the Berkshire town.
In 2016, he was hired as a consultant by the billionaire sports mogul, who also owns Newcastle United Football Club and given the job of managing the Sports Direct empire.