Germany and Hanover 96 keeper Enke, 32, who had suffered from depression since 2003, committed suicide on Tuesday by jumping in front of an express train.
His wife Teresa said Enke had gone to great lengths to mask his depression and keep it out of the public eye, adding that he feared if it came out it would be seen as a sign of weakness and would affect his career and personal life.
"After this tragedy we in football must think how we will break the existing taboos," German football federation (DFB) president Theo Zwanziger told Bild newspaper.
"Why did he fear going public with it? Because he was afraid his soccer career, which he loved, would disappear. Homosexual players for example feel the same pressure.
"If we are to be true to Robert Enke then we must arrive at a point where every player can live without fears. With their strengths, weaknesses and their preferences," added Zwanziger.
Enke's funeral is on Sunday with a memorial service planned at Hanover stadium.
"There should only be one taboo. That of the dignity of the human being," said Zwanziger. "Exclusion, defamation and wrongly understood heroism are undignified and should not be part of that."
