The report said the group was looking to cash in on the rising customer demand for so-called click and collect services, where customers buy goods online and then pick them up from a shop.
The Sunday Times report, which cited property landlords and a source familiar with the proposals, said the offer saved consumers from having to wait in for home deliveries. Some of the sites could be out of town, it said.
No one from Amazon was immediately available for comment.
When Amazon was just selling books and CDs that fitted easily through the letterbox it was fine to be a Web-only business, the source said.
But now it has branched out into everything from children's bikes to electricals it believes it could boost sales by having stores that offer a collection point for shoppers.
(Reporting by Kate Holton; editing by Karen Foster)