The owner of up-market Waitrose grocer and John Lewis department store said its contractual hourly rates of pay have never been below the national minimum wage, but it intends to work with Her Majesties Revenue and Customs to understand if all its arrangements meet the specific criteria of what are some quite "complex" regulations.
It means that thousands of John Lewis staff who worked on hourly rates could be due a top-up.
John Lewis said the amount would cover any payments that might become due, along with employer's National Insurance, pension costs and other associated costs.
John Lewis said it doesn't know how many staff have been affected, but that the £36m is to cover wage payments stretching back six years.
Sir Charlie Mayfield, chairman of the John Lewis Partnership, which also owns Waitrose, added: "Arrangements have already been made to make these payments and contact former partners".
"This arrangement was implemented to support [staff] with a steady and reliable monthly income, but we now believe this arrangement may not meet the strict timing requirements for calculating compliance with the national minimum wage regulations", John Lewis said in a statement.
"We expect to do this as quickly as possible".
It admitted it was not now in a position to give a back pay total, adding its investigation could take some time to complete. His basic salary rose almost 5% to £1.13m but Mayfield requested not to receive his annual bonus, which amounted to £105,000 the year before, and also took a reduced pension supplement.
Its workforce has shrunk to 86,700 from 91,500 in 2016, according to the group's latest annual report, although it said the average number of full-time equivalent employees fell by 600 to 63,300. Mayfield has asked not to receive a rise in basic pay this year.