The investigation relates in part to the "guide" prices that are shown on the supermarket web sites. These are necessary because different local stores have different prices at any one time, but mean that consumers are sometimes charged more than is actually shown on-line, according to reports.
Other complaints relate to the inclusion of unsuitable substitute products for out-of-stock items or the replacement of a luxury item with a cheaper one, but without a refund of the price difference.
There are also concerns that some items purchased on-line are more expensive than those available in-store, and that some orders sent to consumers include products that are very close to their sell-by date.
"We have held confidential discussions with the supermarkets. This is an ongoing investigation," an OFT spokesman told the Independent newspaper.
Representatives from Asda, Tesco and J Sainsbury's have confirmed that they have discussed matters with the consumer watchdog.
Speaking to the BBC, Tesco's corporate affairs director, Lucy Neville Rolfe denied that on-line consumers were being overcharged.
"With a Tesco.com grocery shop your food is picked off the shelves of your local store so whether it is a book you are buying or a carton of milk, you will be paying the same price as you would in-store," she said.