The league’s fixtures have been suspended until April 4 because of the coronavirus pandemic.
And Karren Brady, vice-chair of relegation-threatened West Ham United, says this season’s Premier League could be declared “null and void” given that it could be months before it is safe to resume games.
Newcastle United moved up to 13th place with 35 points after last week’s 1-0 win over Southampton.
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Barber, Brighton and Hove Albion’s chief executive, told the BBC’s Football Focus: "Every league starts with an expectation of completing all 38 fixtures, as it’s in the Premier League, and we want to be able to do that.
"Our intention must be to play the fixtures, but it's really hard to imagine putting on a football game in the Premier League in two or three weeks' time given the scenario we are in.
"If we were to freeze the league it would be incredibly unjust for Liverpool to not be awarded the title, because everybody in the game appreciates what a fantastic season they have had. Equally, it would be unjust for teams to be relegated with nine or 10 games to go in the Premier League.
"I think it's a possible option to leave the 20 teams in the league as it is, but bring the top two in the Championship up.
"It gives us a larger league, with four relegation places next season and then two teams coming up again. It has some merit, but there are a lot of issues to be worked through.
"If we can't complete the season we have to look at radical solutions to get over a short-term hump, as it is."
The Premier League will hold a meeting on Thursday – two days after UEFA meets to discuss the future of Euro 2020 and other major tournaments – to discuss a way forward.
"We've got several teams in self isolation, which makes it difficult to think about that (comeback) date," said Barber.
"So we've got a number of complexities here, which go way beyond thinking of the finances."