Germany captain Michael Ballack sustained an ankle injury in Chelsea's FA Cup final win over Portsmouth last week and will miss the June 11-July 11 World Cup in South Africa, joining injured goalkeeper Rene Adler on the sidelines.
Adler was replaced by Bayern Munich's Hans-Jorg Butt, who was initially seen as third choice, but a strong season has put the 35-year-old in contention for a starting spot.
"We are clear about our decision regarding the team captain and the goalkeeper questions," Low told reporters from the team's training camp in Italy.
Striker Miroslav Klose, midfielder Bastian Schweinsteiger and defender Philipp Lahm are potential captains.
STARTING SPOT
Goalkeepers Tim Wiese of Werder Bremen, Schalke 04's Manuel Neuer and Butt are the contenders for the starting spot with Neuer the favourite.
Butt, however, has played a superb season with Bayern as they won the domestic league and cup double and were runners-up in the Champions League.
Low said he would first inform all his players before announcing his decision, probably on Thursday.
Bayern Munich's seven international players, who lost in the Champions League final to Inter Milan 2-0 on Saturday, will join the squad on Tuesday and Wednesday.
Low must drop three players from his provisional 26-man squad before finalising the squad by June 1.
"This is an extremely difficult situation because I have seen that all players work unbelievably hard, they are eager to learn, are constantly alert and they are investing everything they have in training," Low said.
"At the moment I must be honest. I cannot decide who will go home," he said.
Germany face Ghana, Australia and Serbia in the tournament's group stage.
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