Kinsella, who was appointed to the Senate in 1990 on the recommendation of then-Progressive Conservative Prime Minister Brian Mulroney, has served as speaker since 2006.
His term was set to expire on November 28th — his 75th birthday — but he reportedly wants to retire before the clock runs out, and not be ejected automatically after aging out.
Prime Minister Stephen Harper is expected to announce Kinsella's successor — widely rumoured to be Conservative Senator Pierre Claude Nolin — later today.
Unlike the House of Commons, Senate speakers are not elected by fellow senators, but selected by the governor general based on the advice of the prime minister of the day.
Nolin has served as Speaker pro tempore, or deputy speaker, since 2013, when he was unanimously elected to the post.
Earlier this year, he publicly challenged his Red Chamber colleagues to take a less partisan approach to their work.- Tory Senator Pierre Claude Nolin urges colleagues to be less partisan
"It’s easier for a senator to do his job if he makes decisions less based on partisanship,” Nolin argued.
“Free choice for everyone is often a better guide.”
Nolin favours legalizing pot
He also made headlines in 2002, when he served as chief spokesman for the Senate committee on illegal drugs, which called on Jean Chretien's Liberal government to legalize marijuana.
In 2012, his staunchly anti-prohibitionist views led him to oppose the Conservative government's omnibus crime bill, C-10,which included measures to impose lengthy minimum sentences for some drug-related crimes.
"Prohibition of cannabis causes more harm than the substance itself," he told his colleagues during debate on the bill.
"I repeat: Prohibition of the substance is more harmful than the substance itself."
The only long-term solution, he argued, is to "get rid of prohibition."
"But that is not what we will do with Bill C-10," he noted. "At least use the short-term solution; do not touch it. Keep the status quo."
Meanwhile, Senate insiders predict that Conservative Senator Leo Houssakos — like Nolin, a Quebecer — will likely take over as Speaker pro tempore.
On Tuesday, Auditor General Michael Ferguson told reporters his office's audit of Senate travel and living expense claims has finished gathering information from senators, but isn't yet complete. He said auditors are aiming for the first part of 2015, possibly finishing by the end of March.