Sigma Healthcare has started a contest to buy pharmacy operator Australian Pharmaceutical Industries and claims to have trumped Wesfarmers' offer.
Sigma on Monday proposed buying all shares in the Priceline and Soul Pattinson chemists owner in a deal worth about $773 million.
The offer would pay 35 cents and 2.05 Sigma shares for each API share.
Sigma claimed its offer was worth $1.57 per share, based on the most recent closing price of Sigma shares.
Wesfarmers, which owns Bunnings and Officeworks, earlier this month raised its bid from $1.38 per share to $1.55 per share.
Boss Rob Scott at the time said API would form the basis of a healthcare division. He saw opportunities to expand the product range, improve online shopping and the supply chain.
API on Monday said the Sigma proposal was likely to be more favourable than the Wesfarmers one.
Sigma will be given the chance to examine the API financial books to help finalise the offer.
Sigma said the acquisition would broaden its revenues and customer base.
The company claims a merged entity can save at least $45 million per year.
API shares on the ASX were up 5.12 per cent to $1.54 at 1145 AEST.
Sigma shares were higher by 3.36 per cent to 61 cents.