Heavy investment in players since Todd Boehly came in as owner has not yet been followed by success on the pitch, with Chelsea a disappointing ninth in the Premier League.
Thomas Tuchel was sacked in September and his replacement, Potter, is battling to prove he can be the coach to deliver strong results and trophies to Stamford Bridge.
Now Gilbert Enoka is heading to the London club after making an impressive impact in rugby union with New Zealand over the past 20 years.
Enoka, who stepped up from being mental skills coach to become leadership manager with New Zealand, will join up with Chelsea on what New Zealand said was a "short-term consultancy basis".
The incoming expertise should be a boost to Potter, with the widely acclaimed Enoka having been part of an All Blacks set-up that won Rugby World Cup titles in 2011 and 2015.
Chelsea have spent around £600million on new players in the past two transfer windows, without their sprees having had any obviously positive effect on results, and installing a positive mindset appears to be what they are looking at achieving.
Enoka revealed in early 2017 how his famous policy functioned within the New Zealand ranks, saying: "A d***head makes everything about them.
"We look for early warning signs and wean the big egos out pretty quickly. Our motto is, 'If you can't change the people, change the people'."
Prior to his sacking at Chelsea, Graham Potter revealed his mental health and family life had suffered as a result of the pressures of Premier League management.
West Ham's David Moyes also discussed the impact of being an under-fire Premier League boss, citing the harmful effects media scrutiny can have.
But Bevan, who has been in his role since 2008, believes the LMA is doing its bit to help top-flight managers cope with the strain.
"I think since COVID, the world of sport, not just football, has put health and wellbeing at the forefront of all decisions," Bevan said when speaking to Stats Perform at the Football Business Awards.
"Certainly, in the LMA, we have two in-house psychiatrists and two in-house psychologists.
"It's not just about the managers and coaches, it's looking after the people that work in that environment. We are very, very active in making sure that communication and the services that we offer are utilised as much by the families as well as by the coaches and the managers.
"So it's really important to be as well as physically fit, emotionally fit, and mentally fit, in order to do the jobs, whether you're a coach or working in any environment today."
There has been a record number of managerial dismissals in the Premier League this season.
One of those, Patrick Vieira's sacking by Crystal Palace in March, left the Premier League without a black manager.
Bevan explained the LMA is encouraging clubs to diversify their coaching staff.
He said: "From our perspective, it's making sure that we have a very vibrant pipeline of coaches coming through.
"We're pushing the stakeholders to have a far greater number of coaches from diverse backgrounds that have, for example, the [UEFA] Pro Licence, so that pipeline which the employers are looking at can make a difference over the next five years."
As of the final day of the 2022-23 season, 10 Premier League bosses are from overseas, while the competition has been won by a foreign manager in each of the last 10 seasons.
Bevan lauded the impact managers from other countries had brought to the English game, adding: "They all bring excellence.
"I think we're very lucky that the Premier League and, indeed, all of our leagues are immensely popular around the world, and they attract overseas owners, overseas coaches, and overseas players, so ensuring that the very best in their profession I work in our leagues is really special.
"We're really grateful that we have a really diverse mix of managers and coaches."
The former Chelsea boss has not been out of work since leaving the Blues in April 2023 after just seven months in charge at Stamford Bridge.
Potter began his professional management career with Swedish side Ostersund, who he guided from the fourth tier into the top flight and Europa League during his seven-year spell.
The former defender then spent a season with Swansea City, before a successful three-year stint with Brighton and Hove Albion.
Speaking at Leeds Beckett University, where he was receiving an honorary doctorate, Potter revealed his desire to get back in the dugout.
"Now, I'm in that good place where I'm happy to be ready and looking forward to the next challenge," he told Sky Sports.
"I've had a great break. The journey from where I started to where I finished doesn't come for free. It involves moving to three countries, with a young family, and all that comes with being a football manager.
"It was important for me to take a break, reflect and re-energise. It's been a good time to look at other things, other sports, other teams and visit places.
"I feel really ready, really excited to be back when the right opportunity comes."
Potter is one of several names linked with replacing Gareth Southgate, who resigned as England's head coach following their Euro 2024 final heartbreak against Spain.
While the 49-year-old refused to discuss the possibility of him taking over the reins, he paid tribute to the outgoing Three Lions boss, who led them to successive European Championship finals and a World Cup semi-final during his eight-year spell.
"Today is not the day to speak about [the England vacancy]," he added. "I'm proud of the job Gareth Southgate did.
"As an Englishman in football, I don't think there's anybody who has more respect than he has; how he conducted himself, him and his staff, qualifying for tournaments, going deep into tournaments, getting the country behind the team.
"He's done an amazing job. I'd like to wish him well. I hope he has a nice break, and wish him well for whatever he decides to do next."
