Full-back Lahm ended his international career a World Cup winner, the 113-capped defender going out on a high after Low's men reigned in Brazil.
Kicking off the post-Lahm era for Germany is a World Cup final re-match with Argentina in Dusseldorf on Thursday, with all eyes on Low to see who we throws the armband to.
Neuer said while he is keen to assume the leadership responsibility, he was not about to select his order of preference publicly.
"We have a lot of players that have already been captain. A few of them have been on the team council but there are also players like Bastian Schweinsteiger, Sami Khedira or myself,"
"We now have the experience of winning the World Cup. So there are more players coming to the fore to take responsibility and replace Lahm and Miroslav Klose.
"The manager must decide if a goalkeeper is the right player to be captain.
"There will be many discussions in the next days. But for me it doesn't matter if I am captain or not. I will be in charge anyway. But I am sure there will be a good decision.
"If the manager wants me to be the new captain I will do it. But first we have to look at the whole situation."
Germany also open their Euro 2016 qualifying campaign against Scotland in Dortmund on Sunday, and Neuer said it is close to the Scots' "match of the year".
"I think it wouldn't be an easy match. For Scotland maybe it's the match of the year against us. They will give their best and cause us in trouble," the Bayern Munich shot-stopper said.
"We have to do our job and play well after the match against Argentina during the week. Our team has changed a little bit.
"But we will train later and then tomorrow we will have our final preparations."
