The founder of retail investment giant Baugur, which is now in administration, is understood to be setting up a Kwik Save-style chain called Best Price Foods similar to the Bonus chain he runs in Iceland.
Booker CEO Charles Wilson denied press reports that his company had agreed to supply the venture, although he said it was possible Johannesson could use his cash & carries.
"We are not supplying it as far as I know, although if he approached us we would look at it," he said.
Although Johannesson is non-executive chairman of Iceland Foods, Iceland CEO Malcolm Walker said it had not crossed his mind to seek to stop Johannesson's plan and did not view it as a conflict of interest.
"If he is opening a store it is not real competition for us," said Walker. "He has wanted to start a retail business in the UK for a long time."
Johannesson was not available to comment.