Arsenal midfielder Ozil did not join team mates on Monday in Duesseldorf for the first time since their World Cup victory 50 days ago and will fly in on Tuesday after nursing a minor injury.
"It looks very tough for Wednesday for Mesut," Bierhoff told reporters. "Hopefully, he will be fit for Sunday."
Ozil is one of 18 World Cup winners called up in the 21-man squad for the World Cup final rematch against the South Americans and Sunday's first Euro qualifier in Dortmund.
Some 40,000 fans turned up for the team's first open training since the World Cup victory, with players kicking footballs into the stands and giving away presents.
"It was our wish to give fans and especially the young ones the chance to see their stars from close up," Bierhoff said.
"For us it was a good feeling to kick off our post-World cup season with such a reception.
"This fourth (World Cup) star belongs to the entire country and that shows that we are Germany's team," Bierhoff added. "But now we need to take it forward. We want to keep having positive performances."
Coach Joachim Loew will have to make changes to his starting lineup with striker Miroslav Klose, captain Philipp Lahm and central defender Per Mertesacker having retired from international football.
"We have to hit the ground running," said keeper Manuel Neuer, among the candidates to replace Lahm as captain. "We have to have a good match against Argentina to prepare for Scotland because the team will be slightly different.
"It is very important for us to start our qualifiers with a win over Scotland on Sunday," said Neuer.
Germany are in the European qualifying Group D along with Georgia, Poland, Gibraltar, Scotland and Ireland.