Infantino will stand for re-election as Fifa president for a third time in March, and as yet no credible candidate has emerged to challenge the Swiss-Italian.
Former Tottenham and Switzerland defender Ramon Vega has said he intends to run, but it appears unlikely he will get the five letters of support from member associations let alone be a serious contender.
Senior figures within European football have told BBC Sport they want former Arsenal manager Arsene Wenger to run.
But it is unclear whether Wenger would be prepared to give up his position as Fifa’s global head of football development for a fight against his boss that he may not win.
Hewitt accepted Uefa – and Infantino’s other opponents around the world – must find someone to put their name on the ballot before the deadline of 18 November.
She also indicated it would be important for the president to have a rival after being re-elected unopposed in 2019 and 2023.
“I think it’s important to Gianni to have somebody who stands with a different manifesto, and good for Fifa to have that choice,” Hewitt added.
“We’re in a democracy here. We must remember there are 211 associations and it’s really important that all 211 associations have the opportunity to vote according to how they feel.
“This is somebody first and foremost who puts football first right at the heart of everything that they do. Secondly, it has to be somebody who unites the world. Thirdly, somebody who needs to have the courage to bring about reforms.”
Hewitt said Balogun avoiding a suspension after being sent off at the World Cup was one of the “biggest issues”.
Balogun’s ban was suspended after US President Donald Trump asked for the decision to be reviewed.
BBC Sport understands a proposal was put to the Council to amend the Fifa disciplinary code, which would prevent a repeat.
Under that, regulations would be amended to state the disciplinary committee could not suspend an automatic one-match ban for a red card.
“What happened in July did not serve football… whether it’s the Balogun case, the FFE case… the reputation of football was put under serious threat,” said Hewitt.
“Once behaviour starts to influence what happens on the pitch, then I think it’s a dark day for football and a number of people said that in the room.”
The Fifa Peace Prize – awarded to President Trump – was also raised, but Hewitt said Infantino’s behaviour with “other maybe celebrities and dignitaries” was also discussed.
“When he puts other dignitaries in front of his 211 associations, then he’s lost what football is about,” Hewitt said.
“And that was said by a number of people, not just the Europeans.”
How the Peace Prize came to be awarded will be the subject of an investigation by the Fifa social committee.
“They will consider, first of all, how the Peace Prize came about, whether it should have come about, whether it should have been awarded in the way that it was, who made that decision and whether or not it should be taken out or whether it should be reformed,” Hewitt said.
“That committee will report back to Council in December and then Council will make the decision based on its recommendation.
“Today there was a watershed moment where it’s very clear in order to move forward, which we all want to do, we have to understand the past.”