In the run-in to Friday’s vote, Mr Casey has come to greater public attention thanks to a string of controversial statements about Travellers and social welfare.
The businessman has denied accusations of adopting Trumpian-style tactics to boost his profile.
On Thursday, the eve of the election, bookmakers Paddy Power had cuts the odds of victory for Mr Casey to 16/1, down from 200/1 last week – putting him second only to incumbent President Michael D Higgins.
He has displaced fellow former Dragons’ Den star Sean Gallagher, who has fallen out of favour.
A spokesperson for Paddy Power said: “Peter Casey started out as a complete no-hoper and was dead-last in the betting when he first threw his name into the ring.
“He was a massive 500/1 shot when he secured his place on the ballot paper in the outright market. Now he’s second favourite.”
The Independent candidate temporarily suspended his campaign last weekend after saying he did not believe Travellers should be considered an ethnic minority.
Speaking on the Independent.ie Floating Voter podcast, Mr Casey said Travellers were “basically people camping in someone else’s land” and claimed “they are not paying their fair share of taxes in society”.
Mr Casey faced widespread criticism for his comments, including from his fellow presidential contestants.
The businessman has also suggested the Republic is a “welfare state”.
Writing in an open letter in the Sunday Independent the country had become a “nation of people who expect – no, demand – that the State looks after them”.
The Republic’s Social Protection Minister Regina Doherty has accused the former ‘Dragons’ Den’ investor of “breath-taking ignorance”.