Veteran Liberal MP Simon O'Brien has ruled out becoming president of the Upper House, saying there is no way he would hand over his vote to Labor with the numbers as tight as they are.

Mr O'Brien only found out he had been re-elected to the Legislative Council yesterday, a fortnight after the state election.

The MP said speculation he could find a Labor Party offer to become president too good to refuse had been hurtful and without foundation.

"I want to make it quite clear that I'm not interested in giving over a vote to the Labor Party. Anybody that might think that doesn't know me very well."

"There's no chance."

Labor strategists had been hoping to convince Mr O'Brien to take on the role of president.

With him in the chair, the Government would get an extra vote on the floor, and with Greens support — a working majority.

The president only gets to vote in the event of a tie.

Premier Mark McGowan would not say whether Labor was preparing to put the feelers out among Liberal MLCs.

"That's got a long way to go, the changeover isn't until May 22," he said.

"We'll have those conversations and we'll seek to have someone experienced in the chair but that's something that my Upper House colleagues will no doubt have discussions about."

Government should install first female president: O'Brien

Mr O'Brien said the precedent was for the Government to nominate one of its own for president.

"We would hope that the Labor Party recognise that they've got a responsibility in government that they provide the president in the house of review."

"They've got a number of potential candidates, Adele Farina, Kate Doust, either of those would be acceptable I'm sure to the house."

"You'd think the Labor Party would want to take the opportunity to produce the first female president in the history of the council."

The Legislative Council, which was founded in 1832, has never had a female president.

The Premier has already announced Kate Doust as either its next president or deputy — the outcome of which will depend upon whether any Liberals accept the top job.