The supermarket giant has made a "possible offer" of 161.3 pence per Home Retail Group share.
As part of the cash and shares deal, Home Retail Group shareholders will own about 12% of the combined group, if it gets the go-ahead.
Home Retail Group said it "believes in the prospects for the standalone company", but the possible offer provides an "attractive opportunity" for its shareholders to receive full valuation for their shares.
However, the sale of Home Retail Group's DIY chain, Homebase, to Australian business Wesfarmers is said to be a condition of the possible offer by Sainsbury's.
The £340m deal, which will see the Homebase name replaced by the Bunnings Warehouse brand, is still awaiting the approval of shareholders.
Sainsbury's had until 5pm on Tuesday to make a fresh bid for Home Retail Group after its £1bn offer was rebuffed in November.
The company said previously that it could could shut a raft of Argos stores and relocate them within its supermarkets if the deal was given the go-ahead.
Retail experts believe between 150 and 200 Argos stores could be impacted.
The supermarket has already been working in partnership with Home Retail Group 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 with strong heritages.
Home Retail Group's shares fell 3% in early trading to 148.1p, while Sainsbury's share price also dipped 0.6% to 243p.
The companies confirmed that they have agreed a three-week extension on the deadline of the deal to 5pm on Tuesday February 23 in order to complete the due diligence on the proposed offer.
If approved, the combination of the two companies would trigger EBITDA synergies of about £120 million in the third full year after the deal is complete, Sainsbury's said.
It is estimated that about a half of the savings will be found by relocating Argos stores into Sainsbury's supermarkets as concessions, as well as launching new Argos concessions and expanding Sainsbury's click and collect service.
It also expects to deliver a third of the savings by removing back office functions which overlap between the two companies and by selling Sainsbury's clothing and homeware products to Argos customers.
The supermarket said that, in order to bring the savings to bear, it will face a one-off costs of about £140m, split equally over three years.
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