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 on June 16
The key trio have all been carrying injuries following the end of Bayern Munich's season and are not yet taking part in full training at Germany's pre-tournament training camp.
Low hopes to have captain Lahm back in the coming days, but his club-mates 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 on 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 added.
"In 2010 we showed the players footage of how the fans celebrated like mad back in Germany. It gave us a lot of belief."