Brighton say they are against playing the remaining Premier League games at neutral venues because it may affect the “integrity of the competition”.
Top-flight clubs have been told that using up to 10 neutral venues will be the only way to complete the season.
Brighton chief executive Paul Barber said his club were “not in favour” of the proposal.
West Ham, who are also just above the relegation zone, want to play their remaining home games at London Stadium.
Crystal Palace chairman Steve Parrish says football needs to “at least contemplate whether it’s possible” to resume using measures such as neutral grounds.
The Premier League has been suspended since 13 March because of the coronavirus pandemic but all clubs are committed to playing the 92 remaining fixtures of the 2019-20 season if and when safe to do so.
A major factor in the decision to require neutral venues is reducing the chance of fans congregating, and the selection of grounds will be largely based on a rating from the police and the Sports Grounds Safety Authority.
Not all of the proposed eight to 10 neutral venues will necessarily be Premier League grounds, although the vast majority will be.
Barber said clubs “must all be prepared to accept some compromises” and that Brighton “fully appreciate why playing behind closed doors is very likely to be a necessary compromise to play our remaining games”.
However, he added: “At this critical point in the season, playing matches in neutral venues has, in our view, potential to have a material effect on the integrity of the competition.”
West Ham, who are 16th in the table and only clear of the relegation zone on goal difference, want to play their remaining five home games at London Stadium but feel this does not set them apart from other clubs with major goals still to play for.
Writing in the Sunday Times, Parrish said playing the remaining games would give every club “a fair crack at the best league position they can achieve”.
“Football is just another industry trying to get back to work,” he added. “It doesn’t have any more right to do so than construction or retail, but nor does it have any less.”
Southampton chief executive Martin Semmens told BBC Radio Solent that it would not be appropriate for the Premier League to plan for an immediate return.
However, he said the league and clubs “must plan for how we will bring our business back, otherwise there will be no business and there will be no football club”.
‘Obvious disadvantages’ to not playing at home – Barber
Brighton are 15th in the league, two points above the relegation zone, with nine games left to play – including home fixtures against Arsenal, Manchester United, Liverpool and Manchester City.
“Five of our nine remaining matches [are] due to be played at the Amex – all five matches are very difficult but four are against some of the biggest clubs in European football,” Barber added.
“The disadvantages of us not playing the league’s top teams in our home stadium and in familiar surroundings, even with 27,000 Albion fans very unlikely to be present at the Amex, are very obvious.
“Clearly, we must accept there may also be some benefit from playing our remaining four away matches at neutral venues but the fixture list simply isn’t equally balanced at this stage of the season, and we didn’t play our first 29 matches of the season in this way. So, in our opinion, one thing doesn’t cancel out the other.”
Proposals will make games ‘safer’ than supermarket – Parrish
Palace are 11th in the league on 39 points, 12 points clear of relegation and nine points behind Chelsea in fourth, with nine games to play.
Parrish said he agreed with La Liga president Javier Tebas, who after the French football season was abandoned said he did not understand why “there would be more danger” in football resuming behind closed doors than industries like manufacturing and fishing restarting.
“I’ve seen all the proposals for training and travel and, while there are challenges, those proposals offer a level of protection to players, staff and officials that I believe will render Premier League football one of the safest places in society to co-exist, much safer than a journey to the supermarket at present,” said Parrish.
He added that the issues facing football could be in place for months and affect next season so “the more we can work out now, the better chance we have of coming out of this with the game we all love in position to recover over time”.
However, Parrish said that football would not unnecessarily occupy NHS resources or “take testing capacity from one person in greater need”.
He added that the “issue of player and staff welfare has to be treated with the utmost seriousness”. Manchester City striker Sergio Aguero has said players are “scared” about returning to action amid the pandemic.