"Some people have an issue with Eugene Jones," Ford told reporters on Tuesday afternoon. "I support Eugene 100 per cent."
Jones officially joined TCH as its president and chief executive officer in June of 2012.
Ford said that Jones has done "a phenomenal job" while leading the organization.
The mayor made his remarks hours ahead of an in-camera TCH board meeting, in which board members are expected to discuss Jones’s future at the organization.
The Toronto Star has reported that TCH board chair Bud Purves called in outside counsel last week to probe allegations about actions that management had taken, including Jones.
The Star has reported that management attempted to keep the salary of Jones’s executive assistant from being disclosed on the so-called Sunshine List.
A second allegation the Star has reported is that Jones fired a TCH executive — whom he said resigned — and paid her severance.
While Ford did not publicly elaborate on allegations involving Jones, he said that to his knowledge, the person or persons behind them have not been publicly identified.
"Whatever these allegations are, I’d like these people to come forward and show me the allegations," Ford said.
"There will be a meeting tonight to find out if there was any wrongdoing. I don’t believe there is, but we will investigate it and take it from there," he added.
The mayor told reporters that Jones has his full support and "will not be dismissed as long as I’m mayor and we’ll take it from there."
However, it is the board that would decide whether Jones holds onto his job, not the mayor.
Ford said he had spoken to Bud Purves, the outgoing chair of TCH’s board of directors, who told him that "these are only allegations."
Ahead of the pending meeting of TCH board members, CBC News was told that Jones "remains on the job," though he was absent from a public event celebrating the start of the first phase of the revitalization of Alexandra Park.
Purves was also absent from the event.
CBC News was also told that Jones would not be available to the media on Tuesday.