The owner of the sportswear firm is also considering a 60 million pounds takeover bid for Debenhams this weekend, the Sunday Times said in a separate report.
A formal offer is being put together by him and would come with conditions, the Sunday Times said, citing an unnamed source.
Debenhams secured 200 million pounds in new funds last week but warned that shareholders still face being wiped out unless it secures financial support from Sports Direct, which holds a near 30 percent stake.
Debenhams said Sports Direct needed to either make a firm offer for the group, underwrite a rights issue of new stock, or provide debt funding if it wanted to prevent Debenhams falling into the hands of its lenders.
In a letter to the Debenhams board dated April 5, Sports Direct said it would be willing to underwrite the group with 150 million pounds in cash if Ashley was named as CEO, the FT said.
Sports Direct was not immediately available for comment and Debenhams declined to comment.
Last year Sports Direct bought department store chain House of Fraser out of administration and it has been trying to wrest control of Debenhams for months to further beef up its presence in the sector.
($1 = 0.7667 pounds)
(Reporting by Rishika Chatterjee and Bhargav Acharya in Bengaluru; Editing by David Holmes and Rosalba O'Brien)