Mike Coupe, chief executive of the supermarket chain, made the prediction as Brent crude was being traded at below 50 US dollars a barrel for the first time since 2009.
The industry benchmark has slumped from 118 US dollars a barrel in June and Chancellor George Osborne has warned it is “vital” that deep cuts in global prices are passed on to consumers at petrol pumps, through utility bills and air fares.
Sainsbury’s is one of four supermarkets to reduce prices by 2p per litre on both petrol and diesel this week.
Asked if he saw fuel prices getting to a pound per litre any time soon, Mr Coupe told BBC Radio 5 Live: “If the oil price continues to fall, almost certainly. We have certainly seen prices chased down, mainly by the supermarkets.
“You could feasibly see fuel prices fall below the £1 barrier.”
The energy industry has insisted deep cuts in global prices were already being passed on to customers after Mr Osborne announced a review of the impact on items such as fuel bills, air fares and the forecourt price of petrol.
Ministers said concerned industries were being watched “like hawks” and officials were examining what action might be taken if the fall in the global oil price was not adequately reflected in what the public was charged.
Mr Osborne welcomed a move by four major supermarkets to cut 2p from the cost of a litre of petrol but said more action was required.
After leading a discussion of the issue at Monday’s Cabinet meeting, he said it was “vital this is passed on to families at petrol pumps, through utility bills and air fares”.
Energy Secretary Ed Davey said: “The Government will be watching energy companies like hawks to ensure falls in wholesale gas prices are passed on as quickly as possible to consumers.”
The sector is already the subject of an investigation by the Competition and Markets Authority.
Energy UK chief executive Lawrence Slade insisted cuts in the wholesale price of gas were being passed on in full - with consumers now able to pay £100 less a year if they looked for the best deals.
“Energy suppliers are passing on price cuts to customers.
“When people shop around they can easily find deals that are over £100 cheaper than this time last year and in line with cuts in wholesale energy prices.”
A Treasury spokesman said: “The Government is conducting studies of industries like the utilities and the airlines. We are examining if any action needs to be taken.”
Chief Secretary to the Treasury Danny Alexander told ITV News: “The fall in oil price is a benefit to most of the UK economy provided that the benefits are passed on at the pumps, in the cost of holidays and in the cost of heating homes.
“We also need to support the North Sea oil and gas sector because that is adversely affected by this, it is the biggest industrial investor in the UK.
“So that is why we are also putting in place a more beneficial tax environment.
“But by and large this is a big benefit to everyone else.”
Shadow energy secretary Caroline Flint said: “The Tories have had five years to deal with the problem of energy companies not passing on reductions in wholesale costs and have done absolutely nothing about it.
“Labour has consistently said that the regulator should have the power to force energy companies to cut their prices when wholesale costs fall.
“We need action, not another inquiry. If this Government won’t put an end to rip-off energy bills and give the regulator the power to cut prices, then the next Labour government will.”
AA spokesman Luke Bosdet said if Mr Coupe’s prediction was correct it would be the first time the £1-per-litre level had been breached since the autumn of 2008.
He said the battle for customers between supermarkets was creating “extremely competitive” pricing, with costs at some outlets in some areas pushing towards £1.
However, he added that drivers face a “postcode lottery” with average prices across the country still above 110p per litre.
Tom Lyon, energy expert at price comparison site uSwitch.com, said: “It’s only right that consumers should benefit from lower wholesale energy costs.
“Whilst quick to pass on rising costs, the big six energy suppliers are yet to reduce bills for the majority of their customers who are on standard tariffs.
“It’s now high time for one of the big six to cut their standard prices and help hard-pressed households, and lay down the gauntlet to the others to do the same.
“With the average bill now an eye-watering £1,265 - 168% higher than a decade ago - it’s little wonder that energy costs top consumers’ concerns.
“The best advice for those worried about energy bills is to shop around, as our experience shows that on average most people who do can save over £220 a year.”