Toll Holdings chief executive Paul Little said Australia's largest logistics company had no immediate plans to sell down its 62 per cent stake in Virgin Blue Holdings, the nation's second-largest airline.

He was responding to speculation the Melbourne-based company was planning to offload part of the stake in Brisbane's Virgin Blue in the next 10 days.

Toll, which acquired the stake when it took over ports operator Patrick Corp last year, is evaluating the potential of using the belly space of the carrier's aircraft to expand its logistics business.

"We have been saying publicly for some time now that we are evaluating if and when we should sell all or part of the equity in VBA," Mr Little said.

But there was no formal sale process under way and no decision had been made, he said.

"We have some people helping us, but it is incorrect to be suggesting that we're ready to announce something," Mr Little said.

A senior institutional trader, who declined to be named, said he expected Toll to keep a 25 per cent stake and sell the rest to a trade buyer.

The trader said Virgin Blue shares had underperformed those of Qantas recently as a result of concerns that Toll would sell part of its stake to institutions at a discount, because some airlines, including Emirates, had indicated they were not interested in buying.

It has also been reported that Singapore Airlines, too, is not looking at the Virgin Blue shares.

Both the airlines had not held discussions with Virgin Blue, Mr Little said.