Mr Oakeshott, who defected from the Nationals before the 2003 State election, said he would spend the next few weeks consulting family and colleagues.

The NSW Nationals leader, Andrew Stoner, also confirmed he was considering his options but it is understood he would only run if he was guaranteed the party's national leadership, replacing Warren Truss.

After the federal election, Mr Costello eschewed the leadership, saying he wanted to chase opportunities in the private sector.

He went to the back bench and has hinted that there will be clues to his future in his memoirs to be published in October.

If he stayed, he would almost certainly replace Dr Nelson as Opposition leader, which would upset the aspirant Mr Turnbull.

Liberals who both want him to stay and go have confided all would be easier if he would let people know.

"At that start of the year his intention was to leave. It would be perfectly reasonable for him to restate that," said one MP.

Labor will not contest Mayo and it is likely also to shun Lyne. It could not win either seat.

A senior Labor source said the party would be "mad" to run for Lyne and that Mr Oakeshott would be hard to beat should he stand.

The Liberals are also likely to contest Lyne and they stand a better chance of taking it from the Nationals than they did the seat of Gippsland, which the Nationals retained at last month's byelection.

Lyne will be the third by-election since the federal election and the Treasurer, Wayne Swan, said Mr Costello should decide so any byelection for Higgins would be held on the same day as Mayo and Lyne, saving money.

"It's about time that Brendan Nelson put an end to this by-election farce that's going on, one-by-one, very costly by-elections," he said.

Mr Turnbull said there was no extra cost if byelections were held separately and it was up to Mr Costello as to what he wanted to do.