The 32-year-old Neuer suffered a broken bone in his foot and only returned to training days ago but Germany coach Joachim Loew decided to take four keepers to the training camp in the Italian Alps from May 23-June 5.
"We will see how it goes from day-to-day," Germany coach Joachim Loew told reporters. "What is clear is that without match practice to go into a World Cup is not possible."
"He knows that. We will see at the end of the month or early June how things look and then we will have an honest discussion."
Loew left out midfielder Goetze, who scored the winning goal in the final against Argentina four years ago but has had a lacklustre season.
"We saw that it was not his season, not the normal form with his quality," Loew told reporters. "I think he has immense quality and he has proved this but he was not in that form."
Fellow Borussia Dortmund player Marco Reus' hopes of making his first World Cup got a boost after he made the cut.
Reus, who missed half of this season through injury, was ruled out of the 2014 World Cup after being injured in Germany's last warm-up match. He also missed Euro 2016 through injury.
"Marco is a special weapon, he has special gifts," Loew said of the forward. "He has great intelligence in the game and in the second half of the season he was in really good form. I expect quite a bit from him for the tournament."
Loew also opted to stick with the experienced Mario Gomez as his second-choice striker behind Timo Werner and picked Freiburg's Nils Petersen ahead of Sandro Wagner.
The 30-year-old Wagner has scored four goals in his eight internationals and was part of last year's Confederations Cup-winning team.
Germany face Mexico, Sweden and South Korea in World Cup Group F and will prepare in the Italian Alps from May 23 to June 5 ahead of the tournament in Russia.
Germany play their last warm-up games against Austria a day later and take on Saudi Arabia in Leverkusen on June 8.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
