It comes after a tumultuous week in which Mr Trump admitted he fired Mr Comey at least partially because of the investigation into his team's links to Russia, and after the President passed apparently classified secrets to senior Russian officials.
This has led to heavy criticism by both Democrats and members of his own Republican Party.
As a result, comparison site Oddschecker said that more than four-fifths of bets on the date of Mr Trump's exit have been placed on 2017.
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Odds for a 2017 exit have been cut from 5/2 to as low as 7/4, the site said, and the President is odds-on to leave before 2020.
Paddypower said it was offering 2/1 odds the Trump presidency would crumble this year and 3/1 the billionaire will be impeached.
An Oddschecker spokesman said: "There’s been support for Donald Trump to be ousted from the office before his first term ever since he came into power, however these bets were probably placed out of frustration more than genuine expectation.
"The recent support is definitely note-worthy."
A Betfair spokeswoman said: "Overnight we’ve seen more than £5,000 bet on Trump to leave before the end of his first term and we expect to see a lot more bet today."