The Associated British Foods boss said in a call after the financial results that there was a "working assumption" in ABF that a separation of Primark "is where we would like to get to", although no decision had been made.
Dan Coatsworth from AJ Bell said it was not clear what triggered a rethink by the board, which had previously pushed back against the idea of a break-up, but did say Primark could command a much higher share price as a standalone company separate from its food business, which AB Foods said was "less well-understood" by the market.
Mr Coatsworth said over the years many people have expressed a desire to only invest in Primark, rather than have its rapid growth "diluted" by non-retail interests.
He added that "the wheels are being greased for a corporate break-up", especially as such demergers are "all the rage" at present, with Unilever, Kraft Heinz and Warner Bros Discovery among those currently in the process.
"The idea of 'slimming to greatness' is based on the principle that big companies might benefit from having a tighter focus rather than spinning three or four plates at the same time," he added.
Laura Lambie from Rathbones added that ABF was a "disparate mixture of businesses with no real strategic rationale behind it".
Primark, which has 476 stores in 18 countries, had reached the size where it requires extra focus to capitalise on its growth prospects, particularly overseas said analysts, with one saying Primark was the "jewel" in ABF's crown.
But Primark's challenges in the UK could worsen as Chancellor Rachel Reeves is widely expected to raise taxes in the Budget later this month.
That would come on top of cost rises seen since the last Budget, including more expensive staffing costs as a result of the rise in minimum wage.
People are feeling insecure about their jobs as businesses cut back on hiring, said Laura Lambie from Federated Hermes, and that was part of what was fuelling a "difficult environment" for retailers as profit margins shrunk.
The news comes as a series of casualties on the UK high street continue as the costs of maintaining bricks-and-mortar stores becomes too high amidst rising online competition and pressure on consumer spending.
Recent retail names that have had to close stores or enter administration include Bodycare, Claire's, and Pizza Hut which said it will be slashing the number of restaurants it operates.