The retailing giant is reported to be considering permanently closing up to eight of its 42 stores.
According to national reports, the department chain will announce its decision early next month - around the time it releases its annual results.
The chain closed down eight shops last July, putting 1,300 jobs at risk. They blamed the shift of sales online during the pandemic.
Staff were told they would not be paid a bonus after profits fell by 46 per cent in the first half of year
The centre:mk store is currently temporarily closed as a non-essential retailer. But it has always been a flagship store for the company and an anchor shop at the shopping centre ever since it opened in September 1979.
Prime Minister Margaret Thatcher officially opened the centre and made a tour of John Lewis. She said she was highly impressed by the "vast assortment" of saucepans on offer, and on the good value around the shop.
Mrs Thatcher also praised the achievements of the Milton Keynes Development Corporation and its collusion with the John Lewis Partnership.
John Lewis chairman Dame Sharon White has said it is likely that by the end of the Covid-19 crisis up to 70 per cent of spending in John Lewis stores will be online.
She said the business was battling to cope with customers growing preference for online shopping and that it had too much store space with expensive running costs for the post-Covid trading environment.
If the Milton Keynes store does close it will leave a vast hole in the centre:mk's retail offering as well as being a considerable unemployment blow for the city.
John Lewis Partnership, which recorded a pre-tax loss of £635 million for the first part of last year, has not yet commented on the national media reports.