David Bernstein, the chairman of the Football Association, has said he would be against Sepp Blatter extending his spell as FIFA president.
Blatter, whose fourth term as president finishes in 2015, had said in 2011 that he would not run for the presidency again - but has since suggested that he could try to win a fifth term.
"I would not support that [Blatter seeking re-election], but I'm not going to call for resignations,'' Bernstein told the Culture, Media and Sport Committee's football governance follow-up.
"I stood up strongly last year in terms of the election itself and of proper governance, and I think that's probably helped because I get a real feel of change and reform is taking place within FIFA.
"I'm genuinely encouraged by what I've seen over the past year. There's a real desire and understanding that change has to take place."
Blatter has written to Germany's Bild newspaper in an attempt to clarify controversial comments he made about the country being awarded the 2006 World Cup.
The 76-year-old sparked an angry reaction when he appeared to suggest that there could have been irregularity in the decision to award Germany the 2006 World Cup.
In an interview with the Swiss newspaper SonntagsBlick over the weekend, Blatter said: "Bought World Cups... I remember the award of the World Cup for 2006 when, at the last minute, someone left the room and so instead of the voting being split 10-10 it was 10-9 in favour of Germany.
"I'm glad I didn't have to make a casting vote but, well, that person suddenly got up and left. Maybe I was too good natured and naive."
The remarks were dismissed by Franz Beckenbauer, who was the head of the organising committee for a tournament that was widely hailed as a success for Germany.
"I cannot understand the remarks and suggestions of Sepp Blatter," he told Bild. "He has even got the result wrong - it was 12-11, not 10-9. And what was decisive was that the eight Europeans all united behind us and voted for us."
In his letter, Blatter said what he had meant was not that the vote was rigged but that "you can always find a smokescreen to doubt the legitimacy of a decision".
He wrote: "When asked if I suspected that the 2006 World Cup had been bought, I responded: 'No, I don't presume anything, I am stating facts' and this means that somebody did indeed leave the room during the vote, which Germany won by one vote.
"I don't believe in conspiracy theories - I only believe in facts. As long as there is no clear proof that something illicit was done at any World Cup vote, then you have got to adhere to the legality of the vote. This applies to Germany like it applies to every other nation. That is the main point I was making.''
Blatter was awarded the Order of Merit of the Federal Republic of Germany after the 2006 World Cup - and there are now calls for him to be stripped of the accolade.
Reinhard Butikofer, a Green Party spokesman, told the Welt newspaper: "Sepp Blatter stands for the endemic corruption in FIFA. Therefore, his Order of Merit should be withdrawn."
Blatter is under pressure over the ISL bribery scandal, which has led to calls for him to quit.