Nationals leader David Littleproud has called for divestiture powers to help increase competition in the sector, as households struggle to balance strained budgets with high food prices.
Asked if the government had the power to split up the chains, Mr Albanese replied "no".
"We have a private sector economy in Australia and not a command and control economy," he told ABC radio Brisbane on Thursday.
"We're not the old Soviet Union.
"What we have the power to do is to encourage competition and encouraging new entrants."
Pressure is mounting on Woolworths and Coles over claims of price gouging as living costs soar. (Luis Ascui, Joel Carrett/AAP PHOTOS)
Mr Albanese said a forcible break-up would lead to many workers losing their jobs.
"What we're not about to do is to walk into Woolworths and Coles, which is a concentration of power, and say 'you're going to shut your business here'," he said.
Assistant Competition Minister Andrew Leigh said the government wasn't considering the option.
"We're not looking at divestment powers at the moment," he told ABC's RN on Thursday.
"Where you see them in other countries, they're very rarely used and they're not a priority that we're focusing on at the moment.
"We're really focusing on things that are going to make a direct difference."
Labor has directed the Australian Competition and Consumer Commission (ACCC) to review prices and competition in the sector.
It has appointed former Labor minister Craig Emerson to review the effectiveness of the grocery code of conduct, which governs how the supermarkets treat their suppliers.
Woolworths and Coles have faced accusations of price-gouging customers, stifling competitors and ripping off suppliers.
Woolworths CEO Brad Banducci has announced he will step down from the role later this year. (Dan Himbrechts/AAP PHOTOS)
Woolworth's chief executive Brad Banducci announced he will step down from the top job later this year, which followed a PR blunder on the ABC's Four Corners program, where he walked out of the interview after attempting to retract a comment he made about former head of the ACCC Rod Sims.
Mr Littleproud said the resignation was an "admission of guilt" of price gouging customers by Woolworths and Coles.
"This is straight out of the corporate playbook - blame somebody, make them the fall guy, give them a big payout, put someone in that's within their existing regime and go back to business as usual," he told reporters in Victoria.
"This is a clear breach of faith in the Australian consumer."
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