Speaking on Monday, Hunt said he still believed his party would lose the next election if Johnson remained leader.
The prime minister survived a vote of no confidence by Tory MPs last month.
But he is under renewed pressure over what he knew of allegations about Chris Pincher’s behaviour before appointing him deputy chief whip.
In an interview at the Institute for Government (IfG) on Monday, Hunt was asked if the Tories could win the next election without a change of leader.
“Well I’m on the record as saying no,” he said.
The former health secretary is widely seen to be potting a leadership bid should Johnson be ousted and has repeatedly refused to rule it out.
Asked if he wanted to be leader, he said: “We have to see what the circumstances are and then make the decision on the one.”
Pressed on whether he could win a leadership contest and a general election, Hunt added: “I’m afraid these are very hypothetical questions which I wouldn’t pretend to have got my head around remotely.”
Hunt said the election would be “decided on the economy” not the fallout from the partygate scandal that engulfed Johnson.
“The core reason that ordinary voters vote Conservative is because they think that we will look after the economy better and therefore there’ll be better prospects for them and their families,” he said.
“But at the moment, because of all the global shocks that we’ve had, people don’t feel that confidence.
“I think that the biggest single challenge is to get the economy growing again.”
According to the ConservativeHome leadership contest survey, defence secretary Ben Wallace is the current grassroots favourite to take over as leader.
Penny Mordaunt, the trade minister, is in second place, with foreign secretary Liz Truss in third.
Hunt, who ran against Johnson in the 2019 leadership contest, was in sixth place.