He made the remark during an appearance on the BBC on Friday night.
Although he did not reveal when Brexit would take place if he became the UK's new Prime Minister, Hunt said: "I'm being honest with people."
He was then challenged on whether the UK would still be a member of the EU going into 2020, replying: "I don't believe so."
Sharing screen space, Boris Johnson, Hunt's rival and the frontrunner in the leadership contest, said the UK would leave by October 31 "come what may", and that if this did not happen it would lead to "a huge erosion of trust in politics".
"I think it's very, very important that we get ready to leave on October 31, come what may, and we will," the former London Mayor told the BBC
Up to 160,000 Conservative Party members are voting for their next party leader and Prime Minister to replace outgoing leader Theresa May.
Hunt warned party members not to "vote with their hearts instead of their heads".
He added that the "quickest way" to leave the EU was "to send to Brussels a Prime Minister who can negotiate a deal that will get through Parliament - and I'm that person".
Hunt and Johnson came face-to-face for the very first time on July 9 in front of a live TV audience.
One of the two contenders will succeed May as the new Conservative leader and Prime Minister, with the winner due to be announced on July 23.
This will also be the first time a sitting British Prime Minister has been chosen by party members.
( With inputs from IANS )