The cash-and-stock takeover, worth the equivalent of $1.9 billion or 1.7 billion euros, was pitched at the equivalent 161.3 pence per HRG share.
"The boards of Sainsbury's and Home Retail Group announce that they have reached agreement on the key financial terms of a possible offer for Home Retail Group by Sainsbury's," read a joint statement.
Sainsbury's - Britain's second biggest supermarket retailer after Tesco - now has until 23 February to decide whether to make a formal bid under British takeover rules.
The sale of HRG's home improvements and gardening chain, Homebase, to Australian business Wesfarmers, is a condition of the possible offer. The divestment was announced on 18 January.
If the Sainsbury's takeover goes ahead, HRG shareholders will own about 12% of the combined group.
The group had already made a takeover approach to HRG in November but was rejected.
The supermarket has meanwhile been working in partnership with HRG to test a number of Argos concessions in Sainsbury's stores. The retailer believes the combination of the two companies would create a strong food and non-food retailer.
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