Fagan has taken leave from his position as Brisbane's head coach while new North Melbourne mentor Clarkson's status remains unclear.
Clarkson was Hawthorn's head coach from 2005 and 2021, while Fagan was an assistant coach and general manager of football at the club from 2008 to 2016, before being appointed Brisbane coach in 2017.
Hawthorn earlier this year held a review into claims of historic racism at the club.
The review was performed by external First Nations consultants who did not speak with Clarkson or Fagan.
"This process was ... to speak purely to our First Nations past players and staff," Hawthorn Chief Executive Justin Reeves told reporters on Wednesday.
"We had no idea what was to come out of those conversations so we didn't speak to anyone outside of that group."
The review was delivered to the Hawthorn hierarchy a fortnight ago, with the ABC reporting on Wednesday that a former Hawks player alleged he was told by Clarkson to terminate his partner's pregnancy.
The player said a group of coaches including Clarkson and Fagan urged him to break up with his partner, the ABC reported.
"It's tough reading, it's heartbreaking," Reeves said.
"These allegations are extremely disturbing.
"We are profoundly disappointed that some of our former players and their families feel like this about their experiences at the club."
Reeves said he was unaware of the identities of players interviewed as part of the review due to confidentiality agreements.
But Reeves, who was appointed Hawthorn's chief executive in October 2017, urged the club to face its past.
"Australia has a culture problem historically," he said.
"Like all of us, we focus on every day being better and building a great environment for our club.
"And I feel confident from the report as well that currently our players feel culturally safe.
"But like so many institutions, we have to face our history and our past."