The midfielder is in the midst of a COVID-19 row in Norway.
The country's Health Ministry did not allow the team to travel to their UEFA Nations League game against Romania after one player tested positive.
It is unclear when Berge will be allowed to travel back to England.
If he can make it back in time for the weekend, a negative test should be enough for him to be in the squad for the Hammers game.
"The Norwegian Football Federation believes that we can travel within the regulations," NFF president Terje Svendsen said in a statement about the situation surrounding the team.
"The Norwegian government says no to this. We disagree with that, but of course we cannot defy the government.
"We are very disappointed that the authorities are forcing us to stay home."
Sheffield United told Yorkshire Live: "[we] have a plan in place for all players who are the subject of a covid-19 issue while on international duty."