With the Germans bidding for a fourth world crown, Low's team opened their South African campaign with an impressive 4-0 demolition of Australia on Sunday and next face Serbia on Thursday.
Low is out of contract after the FIFA World Cup and contract extension talks with the German Football Federation (DFB) broke down at the start of the year.
He took over as Germany coach four years ago and led his side to the final of EURO 2008, but his future remains uncertain with the European Championship qualifiers starting in September.
Podolski, who scored the opening goal against Australia, said he spoke on behalf of the squad by saying he hoped Low remained in charge.
"As far as contracts are concerned, now is not the time to talk about it, but all I can say is that both the team and myself would like to keep working with him," Podolski added.
The Cologne forward, voted the Best Young Player at Germany 2006, owes much of his success in the white shirt of Germany to the coach. He has only rarely produced a bad performance for his country, scoring 39 goals in his 74 appearances, while his domestic form in the Bundesliga has been below average.
"I think he (Low) has been delivering the goods for a whole lot of years and for him to be loyal to players, who were on a bit of a downward curve, has paid off."
"I don't think there are many team coaches like him, he has accompanied me for many long stretches of my career, he has taught me a great many things tactically."
Miroslav Klose is just three caps away from his century and his record of 49 goals leaves him as Germany's third-highest goal-scorer. Podolski said question marks over his form in the German media should not have been raised. "If you look at Klose's record, his performances shouldn't even be put into doubt, he has always played at a high level for the national side."