Among those facing the OFT probe are Asda, Tesco and Sainsbury's, after complaints that prices charged online were higher than in their stores.
Other allegations made are that supermarkets use online shopping to offload products that are close to their sell-by dates, and that there are problems with the issue of replacement items when things that are ordered are out of stock.
The OFT confirmed it was examining supermarket pricing online, but said that, because it was an ongoing process, it would not name the companies it had been in touch with. However, Tesco, Asda and Sainsbury's have all confirmed they have been contacted by the OFT.
Separately, a poll of supermarkets conducted by the National Consumer Council has found that Waitrose is the healthiest supermarket in the UK, based on research into the nutritional content of foods, labelling, healthy eating promotions and customer advice.
Sainsbury's came in at number two on the list, while Morrisons and Somerfield lagged at the end of the poll.
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