Philipp Lahm looks set to return to full training soon, but Bastian Schweinsteiger and Manuel Neuer remain doubts for the World Cup opener against Portugal.
The members of the key trio have all been carrying injuries following the end of Bayern Munich's season and are yet to take part in full training at Germany's pre-tournament training camp.
Low hopes to have captain Lahm back in the coming days, but his teammates Schweinsteiger and Neuer are further away from a return.
"Philipp Lahm's ankle injury has improved a lot and he'll start running tomorrow," the 54-year-old said Monday. "Manuel Neuer needs a bit longer to fully partake in team training, (and) Bastian Schweinsteiger is taking things day to day."
Low went on to call on all his squad members to put their club rivalries aside and focus on achieving glory in Brazil, with Germany's World Cup opener against Portugal just 21 days away.
"These guys were opponents, (but) now they're teammates and the work they've done in training has been excellent," he said. "In 2010 we showed the players footage of how the fans celebrated like mad back in Germany. It gave us a lot of belief."
Bayern forward Thomas Muller hailed the level of togetherness in the squad.
"The team is in good shape and is showing a lot of solidarity. There are no small groups, we all have fun together off the pitch even when you take the two groups from Bayern and [Borussia] Dortmund - we all get along well," he said. "So without just speaking for the camera, for now, everything is going very well."