Like Klopp, who will lead the Reds until the end of the season, Hayes will also leave Chelsea in the summer.
The 47-year-old will join the United States women’s team to get a lighter workload in international football and have more time for her son, Harry.
Asked whether Klopp’s announcement felt familiar, Hayes said: “I related to everything he said, yeah, let’s put it that way. I relate to everything he said.
"I don’t think maybe enough attention and time is put on the mental health and well-being of staff in football - definitely.
“I think everybody expects the most from us; players expect the most from us, the club expects everything, everyone expects everything.
“But the volume of hours you have to commit to this job is unsustainable.”
Hayes has faced health challenges in recent seasons, and her football-mad father, Sid, died late last year.
But, in a week where Brighton manager Melissa Phillips was sacked, she said taking time out is not a luxury afforded to female coaches, who are paid much less than their male counterparts.
“He [Klopp] articulated it better than me,” Hayes added. “I don’t have his luxury though, that’s the difference. I don’t have his luxury to make a decision that he can make [to have a full rest].
“Nonetheless, I get to go to an Olympics and a World Cup, so I just have to maybe reflect on how to keep myself as fresh as possible beyond that. But I completely relate to it.”
Chelsea are back playing at Kingsmeadow against Everton in the Women's Super League (WSL) this weekend after a spell of away games and matches at Stamford Bridge.
Hayes gave an update on the status of her squad, adding: “Melanie [Leupolz] will be back in the squad. Ann [Katrin Berger] is still injured, Cat Macario is still injured, Millie Bright is still injured.”