Mr Ashley has until 21 March to respond after a letter from Hartlepool MP Iain Wright.
The letter reveals Mr Ashley had invited the Business, Innovation and Skills (BIS) select committee – which Mr Wright chairs – to a meeting at the company’s base in Shirebrook.
“The treatment of low-paid workers and enforcement of the national minimum wage are issues that the committee will be keeping under review over the coming months,” Mr Wright’s letter states.
“In line with select committees’ commitment to transparency, it is normal practice for the BIS Committee to meet in public at Westminster and we agreed to adhere to this practice on this occasion.
“A number of alternative dates have been offered to you by the Committee Clerk, but… you have not accepted any of them, nor agreed in principle to attend.
“Should you fail in your reply to agree to attend on one of the dates offered to you…the committee reserves the right to take the matter further, including seeking the support of the House of Commons in respect of any complaint of contempt.”
Sports Direct has not responded to the BBC’s request for a comment.
The company has previously pledged to review worker rights, with oversight by Mr Ashley, who also owns Newcastle United Football Club.