Hesson stepped down at the end of the season after six years in the job and applications for his replacement closed yesterday.
Otago Cricket Association (OCA) chief executive Ross Dykes was not giving much away, but he confirmed he had received 15 applications by early afternoon and was expecting "one or two" more.
Horne played his cards close to his chest when contacted by the Otago Daily Times for comment.
"I'd rather not say in the media," he responded when asked if he had applied.
However, the 40-year-old Auckland assistant coach is definitely ambitious.
"Coaching a side at first-class level and above is certainly something I want to do, absolutely," he said.
Horne will be remembered fondly in Otago. An aggressive opener with a trademark high backlift, he transferred south from Auckland and had five seasons with Otago from 1996-97 to 2000-01.
He flourished, scoring 1977 first-class runs in 23 games at an average of 52.0, including seven 100s. He was less consistent at international level, scoring 1788 runs in 35 tests for New Zealand.
But his century at Lord's in 1999 helped inspire his side which went on to clinch a memorable test series win.
He retired in 2006 and said the game has moved on in the intervening years.
"I loved my time as a player but the game and coaching has certainly changed a lot since then. But that is the exciting thing about it.
"And obviously you've now got a purpose built ground [in Dunedin] and a lot of the facilities have improved. You've [Otago] had some success as well, which is always good."
Horne might have some stiff competition from a former Otago team-mate - Matthew Maynard.
Maynard, who played eight first-class matches for the Volts, was tipped as an early favourite for the Wellington job which has also been vacated.
But Maynard has also been linked with the assistant's role with India and might be out of the picture. Former Bangladesh coach Jamie Siddons is thought to be the new frontrunner for the Wellington job but may have also applied for the Otago job.
Canterbury's Paul Wiseman is definitely out. The former international spinner said he considered applying but it was not the right time for his family.
White Ferns coach Gary Stead and Dipak Patel could not be reached for comment. Patel is thought to have applied for the Wellington job and, if the rumour mill is to be believed, Stead has decided against applying for the Otago job.
Volts assistant coach Mohit Rao said he was enjoying his role as assistant and had not applied, and Otago Country coach Andy Sainsbury could not be reached for comment.
Dykes said he would be joined on the interview panel by OCA chairman Murray Hughes, Otago cricket manager Mark Bracewell, New Zealand director of cricket John Buchanan and former Otago captain Craig Cumming.
The five will put together a short-list and seek to interview candidates as soon as possible. Dykes would like to make an appointment as early as June 10.
