Bach would not comment on the announcement by UEFA leader Michel Platini yesterday that he was a candidate to take Sepp Blatter's place as FIFA president when an election is held next February.
But he said in an interview that all candidates had to embrace "transparency".
"That applies to each candidate. It applies particularly because FIFA's problems will not be over with the election of a new president.
"There must be reforms to the FIFA structure, transparency must be improved, the other structures must be transformed. The election of a president alone will not be enough."
FIFA was rocked by the arrest of seven football officials accused of taking bribes on the eve of its Congress on May 27.
Bach spoke at the first day of the congress and called for reforms. The following day Blatter was reelected to a fifth term as president but within four days he had announced that he would stand down.
The seven FIFA officials are among 14 people charged by US authorities of involvement in more than $150 million of bribes for football marketing contracts.
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