Early favourite Ian McCall and former St Johnstone players Alan Kernaghan and Allan Preston have all declared their interest in the McDiarmid Park vacancy.
Ian McCall has a good record in the lower divisions
The Perth club sacked John Connolly after a poor First Division campaign.
McCall was sacked last month by Dundee United but previously led Falkirk to the First Division title.
Kernaghan came close to leading Clyde to the championship before being sacked along with Preston after a short spell as assistant at Livingston.
Celtic and former Scotland midfielder Paul Lambert has also indicated he would be interested - but only after his contract ends in the summer.
But Saints chairman Geoff Brown appears keen to have someone in place by then.
McCall, sacked with United in relegation trouble in the Scottish Premier League, told BBC Sport: "I'm flattered to be linked with the job.
"I'm an out-of-work manager and my record stands up to anybody.
"If the St Johnstone chairman wants to have a chat, I would do that."
Saints chairman Geoff Brown is known to be an admirer of McCall, especially his record at cash-strapped clubs Morton, Clydebank and Airdrieonians before heading for Tannadice.
Brown had a sometimes tetchy relationship with Kernaghan while the Irishman was a defender at McDiarmid Park.
But Kernaghan, who enjoyed a successful spell at the club as they clinched promotion to the top flight in 1997 and qualified for the Uefa Cup, would jump at the chance to replace Connolly.
"Of course I would be interested in taking that job," said the Falkirk defender.
"I wouldn't have thought it would frighten some people off because there is so much promise there.
"They have a good tradition and have the backing from their chairman, so it's a great opportunity for anybody.
"It's unfortunate the way it has came about with John going, but the new manager will have to go and try to change it quickly, but it doesn't hold any fears for me."
Preston, along with Kernaghan from Livingston in November, said: "I spent seven years there and they were very successful and memorable years having got to Europe, winning the First Division and getting into the Premier League.
"It's sad for John, but who wouldn't want to be manager at St Johnstone?
"So it's a club that's obviously very close to my heart and, whoever gets that, is going to get a top job, but it will be difficult considering some of the people that will want it."