Representatives from the Premier League's 20 clubs met on Friday to reaffirm their commitment to resuming the campaign and have reportedly marked June 8 as the time to get back underway.
But Barber does not believe playing on in neutral venues is the correct solution.
Premier League
'We have to play better' - Klopp on Man Utd performance
29/10/2021 AT 13:34
He said in an official club statement: "We haven’t been asked if we would consider our stadium being used as a neutral venue for any remaining Premier League matches - by our colleagues at the league, the government or the police – and at this point we haven’t been approached to have such a discussion either so I am unable to say why our stadium has been included in the reports.
"We do of course understand that in the very difficult circumstances we are facing that every option must be considered – but that should only be when safe to do so for all concerned and, if and when we reach that point, we are not in favour of playing our remaining matches at neutral venues.
"Clearly, we must all be prepared to accept some compromises, and we fully appreciate why playing behind closed doors is very likely to be a necessary compromise to play our remaining games while continuing to fully support the government’s efforts to contain the spread of coronavirus.
But 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.

Liverpool are leading the race for Koulibaly - Euro Papers

Barber believes taking away home advantage for clubs near the bottom of the table places them at a competitive disadvantage.
He continued: "Five of our nine remaining matches 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.
"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.
West Ham, who are 16th in the table and are only above the relegation zone on goal difference, say they would prefer their home games to be played at the London Stadium.
The BBC report a growing number of Premier League clubs are open to playing the remaining fixtures at neutral venues but only if the threat of relegation is removed.


Writing in his Sunday Times column, Crystal Palace chairman Steve Parish argued for the return of Premier League football.
He said: "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."
Premier League
Spurs 'call off pursuit' for Conte as new manager - reports
04/06/2021 AT 21:35
Premier League
Pogba: Beating Liverpool would put us on their level
15/01/2021 AT 09:52