Chelsea gave N'Golo Kante permission to miss training on Wednesday after the midfielder expressed safety concerns over a return amid the coronavirus pandemic.
The 29-year-old returned to training at Cobham on Tuesday, the first day Premier League clubs were allowed to resume small group sessions, but decided against training again on Wednesday.
Kante lost his older brother to a heart attack just weeks before the World Cup in 2018, while a few months earlier the player himself fainted in training before being given a clean bill of health.
Watford captain Troy Deeney is also skipping training over concerns for his son's health, as well as that of BAME players.
The Professional Footballers' Association has asked the Premier League to conduct further research into the effect of coronavirus on players from ethnic minority backgrounds.
Data from the Office of National Statistics suggests black men and women are almost twice as likely to die from coronavirus compared to white men and women, even when factors such as health, disability, household composition and area deprivation are taken into account.
Deeney's team-mate Adrian Mariappa was one of six positive results to come back from an initial batch of 748 tests covering both Premier League players and non-playing staff, with two members of Watford staff and Burnley assistant manager Ian Woan also testing positive.
Jamie Redknapp told Wednesday's The Football Show he was concerned about the Premier League losing its level playing field if a significant number of players decide against training - and said he believed "a lot more" could follow Deeney's and Kante's lead.
He said: "Some managers have come out now and said it's going to be a fair situation no matter what happens, but if you're going to lose three or four players, and Troy Deeney's the captain of Watford, that's not a fair competition.
Neville: Some players uncomfortable with next stages
Gary Neville warned on Tuesday that more players may reject a return to Premier League training, while Jamie Carragher said he was increasingly confident that the league will resume this summer.
"I know there are Premier League clubs with five or six players who don't want to return or are uncomfortable with certain things around stage two or three," Neville told The Football Show.
"We do have more problems and issues to resolve over the coming weeks."
Meanwhile, Carragher doesn't believe the reluctance of a small number of players to return to training is likely to derail plans to resume the Premier League season this summer.
He said: "We have always said on this show that if a player does not feel safe or sound to go back, he can't go back. This was always going to be the case that maybe one or two players in every squad may not feel safe and may not want to go back.
"I do not think that would stop the Premier League going on. If players en masse said they did not want to be involved, then that would be a big problem.
"But if one or two players in every club, that is something the clubs and Premier League will just have to accept and try and get them on board going forward."
Notebook: What next after return to training?
Sky Sports News reporter Geraint Hughes looks at what's next in the government's protocol…
The work behind the scenes to enable 'Step 1' of the return to training protocols to happen safely was complex, and involved a huge range of medical professionals, sports administrators and government officials.
Step 1 is witnessing a tentative and measured return to training. It has to be, the rules are clear; however, it's limited as to what footballers and other sportsmen and women can actually do.
So should Step 1 not encounter major obstacles such as a substantial rise in the number of positive tests for COVID-19, or coincide with a general increase in positive tests among the public as some return to commuting and work in their lives, then Step 2 of the return to training protocols becomes more of probability than a possibility.
Is there such a massive difference between Step 1 and 2? Yes, huge. Step 2 allows for the wonderfully-worded phrase 'social clustering' to be cleared for all sport. In reality, this is the bit which Premier League managers are most looking forward to as it allows contact.
At the moment, only two footballers can be within two metres of each other at the training ground, but if contact is allowed that brings training sessions back to where reality stopped sometime last March. It opens the door for 11 vs 11, set-pieces, sharing of equipment and it allows tackling.
Maguire: Training felt 'so safe'
Manchester United captain Harry Maguire says it felt "so safe" returning to training this week following the Premier League's first round of coronavirus testing.
United returned to their Carrington training complex on Wednesday - two months since their last competitive match - and, although it was a change from the norm, Maguire was pleased to be back.
Asked if it was reassuring knowing everyone had been tested, Maguire told the club's website: "Yeah, it's been a strange few months, but it has been a protocol which the club has followed. It seems such a safe environment.
"It's our first day back today, but it seems so safe and everyone is respecting it so well, so long may that continue and I'm sure no one will have any problems.
"There is a lot less people at the training ground when we go in. Today I was in a group of four, working with one coach, so not many people.
"You've got a lot space, big areas, not going really close to anyone, but the main thing is getting the work in and it was a tough session, [then] go home and now I'm relaxed and it's all in the bank and I'm looking forward to tomorrow."