Muller has over 100 caps to his name, and an international record that includes 38 goals, 36 assists and a World Cup golden boot in 2010.
The 31-year-old sustained a knee injury during Germany’s dominant 4-2 win over defending champions Portugal which kickstarted their tournament and put their hopes of qualification firmly within their grasp.
“After our match against Portugal, some of the players got slightly injured and that’s why we brought them off the pitch,” Low said.
“Our medical staff had a lot of work to do the last two or three days but this morning, the final training, all those players like Mats Hummels, Ilkay Gundogan, they trained with the team.
“Only Thomas Muller couldn’t, and Lucas Klostermann either. With Thomas Muller we will have to wait until tomorrow, he will do another test tomorrow morning whereas the other players will train here at the hotel.
“And we will see and make a decision whether Thomas Muller will be at our disposal or not.”
Low, who will leave his role in charge of the national side next month after 15 years in charge, hopes the forward will be fit for the game.
“There are different thoughts of course, different options for me to choose between different players, but we will talk to the players, to the team,” he said.
“The team gets to know about the starting line-up first from my side and so we just said we will wait until tomorrow afternoon and then we will take a decision.”
German defender Hummels also stressed the importance of the striker, who was the second-highest scorer for Bayern Munich in the Bundesliga this season behind the prolific Robert Lewandowski.
“In general, (without) Thomas Muller, a leader is missing on the pitch, very communicative, and very positive, he initiates our pressing, has good ideas in attack,” said the Borussia Dortmund man, a former Bayern team-mate of Muller.
“There are not so many characters like him so it will change our game. The qualities that he brings into our game, we will miss them but we can compensate with other qualities and other players.
“With the line-up that we have I think we have a lot of quality to be able to replace him.”
Hungary manager Marco Rossi urged his side to exercise caution as they look to build on their draw against world champions France.
“If we think we can come here and go gung-ho, all-out attack against Germany, we’ll concede six,” the manager said.
“We need to be very careful, we need to be well aware of what our strengths are and of where our weaknesses lie, and we need to produce a tactically flawless performance.”