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.
"We're not the old Soviet Union.
"What we have the power to do is to encourage competition and encouraging new entrants."
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.
"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 to review prices and competition in the sector.
It has also 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.
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