Poloz, who took office in June 2013, said earlier this year that a second term was "one of the options", which would make him the first governor to get a second term since the 1980s.
Eight of 10 economists and market strategists surveyed by Reuters said current Senior Deputy Governor Carolyn Wilkins is the front-runner to take his place.
"I think the general sense is that Poloz has groomed her for the role," said Derek Holt, Scotiabank's head of capital markets economics.
Wilkins joined the bank in 2001 and was appointed to its Governing Council in 2014. She regularly appears alongside Poloz at press conferences and government hearings.
Appointing Wilkins, analysts said, could be seen as Canada staying the course on monetary policy. The central bank has remained on the sidelines even as counterparts, including the U.S. Federal Reserve, have eased interest rates.
Unlike some global peers, Canada's inflation rate is near the central bank's 2% target.
The Bank of Canada declined comment, while the Prime Minister's office had not yet responded to a request for comment.
The bank's board of directors oversees the selection process of a new governor, but the finance minister and the prime minister have the final say.
"I cannot see this government not appointing a female," Carleton University associate professor Ian Lee said, noting that past governors were all white males. Prime Minister Justin Trudeau's government has a gender split cabinet and a history of appointing women to key positions.
However, the last three Bank of Canada governors were brought from outside the central bank, and front-runners often have been passed over.
"There have been lots of surprises in these choices in recent go-arounds," said BMO Capital Markets chief economist Doug Porter.
Many thought Tiff Macklem, then a senior deputy governor, would succeed Mark Carney as governor in 2013, but he lost out to Poloz who joined from Canada's export credit agency.
Macklem - who left the bank in 2014 and is dean of a top Canadian business school - is seen by some as a major contender for the role, particularly if the outlook for the economy sours.
"Just as Canada relied upon Carney's background, credibility, and connections to steer through the last crisis, we may yet require a battle-tested veteran," said Karl Schamotta, chief market strategist at Cambridge Global Payments.
Other potential candidates are former deputy governor Jean Boivin, now head of BlackRock Investment Institute and deputy governor Paul Beaudry, who joined the bank last February.
By Kelsey Johnson and Fergal Smith