A potential problem has arisen for the WA Liberals, already in disarray, with Labor considering offering a former Liberal minister the role of Upper House president.

It is understood the new Government is waiting to see whether Simon O'Brien secures a seat in the Legislative Council, before offering him the role.

If Mr O'Brien accepted, Labor and the Greens could end up with a working majority in the Upper House, based on the count so far.

The president does not get a deliberative vote in the house, only a deciding vote in the event of a tie.

Mr O'Brien, who was first elected to parliament in 1996, was a minister for transport and commerce during the Barnett government's first term.

He was dumped from the ministry in 2013 and was not afraid to criticise the Government from the backbench, particularly on the issue of council amalgamations.

There is deep concern among Liberal MPs that Mr O'Brien may be tempted to accept the position.

Mr O'Brien was contacted for comment.

Liberals due to meet on Tuesday

The established precedent in the Upper House is for the Government to nominate one of its own as president, and for the Opposition to field someone for deputy president.

It is an unwelcome development for the Liberal MPs, already in disarray, over the loss of more than half their members.

They are scheduled to meet on Tuesday morning at State Parliament, to determine who will replace Colin Barnett as leader.

Mike Nahan is a certainty to take on the role, after Deputy Liberal Leader Liza Harvey confirmed she would not nominate in order to devote more time to her two teenage children.