Infantino said the situation at FIFA had been briefly discussed at an executive committee meeting on Thursday and there was a feeling that there should be a united European position.
"There was little bit of a discussion around FIFA matters but let's not forget this is UEFA and we have to focus on UEFA activities," Infantino told reporters.
"We have to make sure we run and organise our confederation in the best and most professional and most democratic possible way.
"There is a feeling of everyone being... really up to here with all these stories," he said, raising his hand to his forehead.
"We have to concentrate on football which is what we are doing, and there is also a feeling of having a united European position on these matters.
"The discussions will go on, it is not up to UEFA to dictate, to take any position, it will be up to the national associations. Some have strong feelings, some have less strong feelings but it's their own free will."
FIFA has been plagued by a wave of scandals and controversy, ranging from allegations of corruption in the 2018/2022 World Cup bidding process to a row over $25,000 (15,954 pounds) watches gifted to executive committee members at the World Cup in Brazil.
Anger mounted last month when a FIFA's ethics report into the bidding process for the 2018/2022 World Cups identified inappropriate and "problematic" conduct by people involved in a number of bids, but found insufficient grounds to recommend a re-vote.
Despite pressure for the full report of the investigation to be published, only a 42-page statement by ethics adjudicator Hans-Joachim Eckert has been made public.
There were even calls for European associations to boycott FIFA, something Infantino said was not discussed on Thursday.
"Every day there is something new coming out, it would certainly be helpful to have once and for all some clarity, as the UEFA president (Michel Platini) has said already," said Infantino.
"It would be helpful as much as possible to publish this report because as long as a only a few people know what is there and some things are leaked here and there," added Infantino, referring to an investigation
"Everyone says a little bit what he wants but without any shred of any evidence of anything...nobody really knows."
(Editing by Toby Davis)
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