JLP is the owner and operator of John Lewis and Waitrose brands.
Stores put up on sale are said to be mostly located in the south of England, with 20-year inflation-linked leases.
The publication reported that marketing of the stores will begin next week.
Property advisory firm CBRE has been selected to represent the partnership during the marketing process.
As of now, there is no certainty that the deal will materialise.
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In October 2020, a five-year self-funding Partnership Plan was unveiled that aims to see JLP reach £400m profit by 2025.
The company will invest capital to update stores, improve prices and increase online operations, including expanding online grocery deliveries.
The news of raising funds with Waitrose stores comes after JLP chairman Sharon White reportedly considered selling a minority stake in the group earlier this year to raise at least £1bn for investment.
Recently, JLP reported its total sales increased 2% to £5.8bn in the first half of the fiscal year (FY) ending 29 July 2023. Sales in the Waitrose division rose by 4% to £3.7bn during the period.
Earlier this month, Waitrose lowered the prices of 250 popular autumn products, marking the third round of cuts this year.
JLP owns 35 department stores and 329 Waitrose shops.