Private equity has cash burning a hole in its pocket and family-owned grocers are high on the shopping list. Property-rich, high turnover and risk-averse, family-owned retailers are attractive because they give private equity options to claw back any debt that would be amassed during takeover.

Sainsbury's, Morrisons and Carrefour are all public companies, but its the management style that a family-run business engenders that makes them appealing. The Sainsbury and Morrisons families each own about 20% of their chains, while the Halley family has a 13% stake in Carrefour - the world's second-biggest retailer.

A CVC, Kohlberg Kravis Roberts, Blackstone and Texas Pacific Group consortium are mulling over an £11bn bid for Sainsbury's, which has property valued at £7.5bn, while billionaire Bernard Arnault and Colony Capital bought a 9.1% stake in Carrefour last week, insisting they are long-term investors.

However, industry observers suggest they are bound to have an eye on the French giant's property portfolio, estimated to be worth £10bn. The scale of the consortium's ambition - a bid could top £34bn and Carrefour's market capitalisation stands at €30.5bn - is not lost on anyone. If Colony can get the Halley family's confidence, a takeover would become a whole lot easier.

"It's the property value that makes these supermarket groups so attractive to private equity," affirms one private fund investor, adding: "Ken Morrison in particular has been very conservative in the way he has managed his property."

Morrisons is sitting on a property portfolio that is more than 90% freehold but it is unclear whether Ken Morrison can be persuaded to yield control.

Keeping it in the family might have conserved its property portfolio, but many believe this factor got Sainsbury's into trouble, says Verdict analyst Alistair Lockhart. "Sainsbury's got complacent. It was slow to react in a changing market and this led them to extraordinary difficulties before Justin King took over," he says.

A family-run business is not without its advantages, however. Lockhart points to King's assertion that Sainsbury's strength is the relationship with its customers and fears this could be lost with a private equity buyout. "Sainsbury's is a British establishment. Whether or not it is down to the family connection, tradition counts and customers care about the brand." The same can be said for Morrisons, which boasts a strong relationship with customers in its homeland. Carrefour, likewise, enjoys iconic status in France.

Yet all three chains are at various stages of recovery, giving them special appeal among private equity groups. Sainsbury's, with a market capitalisation of £9.1bn, is half-way through its recovery programme. While sales are strong, margins could be improved.

Morrisons is seeing the light after three years of painfully picking its way through the fallout of its Safeway acquisition. Valued at £8.2bn it announced its new strategy under new chief executive Marc Bolland this week.

Carrefour is also picking up the pieces after over-expansion into foreign countries. It has pared back costs by selling unprofitable stores, cut prices and is expanding into emerging markets.

But its troubles aren't over. Just last week - hours after the Colony Capital deal was completed - chairman Luc Vandevelde quit after an apparent fall-out with the Halley family.

Private equity is unlikely to be distracted by these kind of concerns and the likelihood of a major supermarket falling, severing its family ties, grows ever stronger.