Sainsbury's said: "The combination of Sainsbury's and Home Retail Group is an attractive proposition for the customers and shareholders of both companies."
Sainsbury's said it was now "considering its position" before a potential second offer.
Under UK takeover rules Sainsbury's has until 2 February to decide whether to make a formal offer.
Former Garden Centre Group chief Nicholas Marshall has expressed interest in Homebase and criticised its online efforts this week.
French home-improvement retail chain Leroy Merlin and South African furniture and household goods retail chain Steinhoff International are also reported to be interested in Homebase.