The Tories want Carney to keep his mouth shut if he vows to stay
Hannan made the remarks in an interview on Radio 4's Today show.
Hannan's demand is the latest volley in an extraordinary fight between pro-Leave Conservative politicians and supporters of Carney over whether Carney favoured the Remain camp before the EU Referendum, and the anti-independence "No" vote in the Scottish Referendum.
Hannan had previously called for Carney to resign.
But late on Sunday it appeared that supporters of Carney - perhaps with the governor's blessing - whispered to the Financial Times and the Economist that he had no intention of cutting his eight-year term short and that he would announce later this week that he intended to defy his critics and stay on.
Hannan changed his tune, slightly. When asked whether Carney should resign he replied "It's up to him," but:
"If you do stay it's important to comport yourself as a quiet and discrete public servant who errs on the side of saying too little."
"It's unimaginable that you'd have Eddie George or Mervyn King intervening across a range of political issues the way he has."
"... it's up to him but if he does stay it's got to be on the basis that he's not the rock star banker who resumes to tell Scotland and Britain which way to vote, but sticks narrowly to his brief."
Most economists give Carney high marks for his handling of the economy and monetary policy.
But Carney has angered some when he has given answers to political questions. Prior to the Scotland independence referendum and the EU vote, Carney made a few, brief, non-detailed remarks about what might happen to the economy afterward. Unsurprisingly, as far as most economists are concerned, he suggested that Brexit was "the biggest domestic risk to financial stability" and that an independent Scotland would not be able to use the pound.
At the same time, as the indefinite low-interest rate environment fails to stoke robust growth or healthy inflation, more critics on the right are starting to voice their dismay at the volume of cheap money - and the debt it creates - being generated by the BOE. Prime Minister Theresa May, former Tory leader William Hague and current MP Michael Gove have all made recent public statements saying they do not like his policies.
Over the weekend, rumours in the press suggesting Carney had become tired of being criticised and wanted to leave early gathered pace.
Then on Sunday, the Financial Times and the Economist both weighed in with multiple stories defending the governor. Their sources suggested that Carney was not going to give up the job or the BofE's independence simply because he has a few political haters.
And former BofE Monetary Policy Committee member David "Danny" Blanchflower stirred the pot with a tweet that suggested the Tories should keep their mouths shut. "Fox Rees-Mogg Davies Hannan Hague Gove are a danger to UK economy they are raising cost of borrowing & lowering GBP every time they opine," he wrote.
We will likely know later this week - perhaps on Thursday when he is scheduled to deliver its quarterly inflation report - whether Carney will stay on until 2018 or 2021.