Hayatou is one of five Fifa vice-presidents who are bringing action against Blatter after Zen-Ruffinen's allegations came out.
Blatter declined to comment any further, saying he would tackle other issues of mismanagement in his written response to Fifa's executive committee.
The English Football Association has already pledged to give its backing to Hayatou.
The FA has been involved in talks with other national governing bodies but came to its conclusion despite backing Blatter four years ago ahead of Uefa chief Lennart Johansson.
An FA statement on its official website said: "The board felt unable to back the current president, Sepp Blatter.
"The FA wanted to place on record its high regard and admiration for the general secretary of Fifa, Michel Zen-Ruffinen.
"In increasingly difficult circumstances, he has continued to seek to fulfil his responsibilities.
"In that task, he deserves to receive the full support of the worldwide football community."