That floor price is an 11 per cent discount to yesterday's $3.65 closing price and would mean the minimum Foodstuffs can realise from the share sale is $101m.
The Herald reported in 2006 that Foodstuffs paid around $150m to buy a 10 per cent stake in 2006.
Foodstuffs' stake in the red warehouse dates back to when the supermarket firm attempted to take over the business.
The Commerce Commission eventually blocked the application for full takeover, leaving Foodstuffs with its stake in the business.
Retail commentator Chris Wilkinson said Foodstuffs' decision to divest would likely have been made based on their knowledge of the retail sector and consumer market and the overall economy.
He said the move was prudent given the headwinds ahead for the retail sector.
Growth in the retail sector and large spending increases have largely been driven by closed borders, but Wilkinson said the levels seen now were likely a peak.
Foodstuffs acquired the stake at a time when The Warehouse first began rolling out its the Warehouse Extra stores, Wilkinson said, back when it was making a push into the grocery market and wanting to leverage grocery to drive visitation to its stores.
The format wasn't as successful as anticipated and in recent years the retailer has focused less on the offering, he said.
"The reason why Foodstuffs are likely to be selling now is the fact that the Warehouse has bounced back from where it was [financially]," said Wilkinson.
"They will be mindful that the Warehouse continues to face challenges across many of their categories."
Shares in The Warehouse fell as low as $1.50 a piece at the peak of the pandemic market melt-down in March last year but have recently traded as high as $3.86 each.
Wilkinson said Foodstuffs likely no longer saw The Warehouse as a threat in its market.
Retail analyst Ed Glennie, investment strategist at Hobson Wealth, agreed - he said that Foodstuffs likely no longer saw the group as having much of a future in food retailing.
"They may not see The Warehouse as much of a threat as they might have 15 years ago."
Glennie said The Warehouse was "still realising value" and was one of Hobson Wealth's top broker picks.
He said analysts were largely pleased with how The Warehouse had traded and its transformation strategy was now delivering results.
The Warehouse, which owns retail chains The Warehouse, Warehouse Stationery, Noel Leeming, Torpedo7 and online marketplace TheMarket, sales for the three months to May 2 were $791.2 million, up 35 per cent on the same quarter last year or 10.8 per cent on FY19.
- additional reporting by Aimee Shaw.