German newspaper Die Welt reported that Infantino had improperly ordered the destruction of the minutes of a Fifa executive committee meeting.
According to Die Welt, Fifa's independent ethics committee is looking into the matter and could impose a 90-day ban on the new president.
Fifa spokeswoman Delia Fischer said the allegations were baseless.
"The email exchange that makes mention of the deletion of audio files refers to a copy of the original audio file of the meeting that was improperly stored on a local drive," she said.
"This mention does not refer to the officially archived audio file. That file exists and is properly saved at Fifa."
A spokesman for the ethics committee's investigatory arm, Roman Geiser, told the AFP news agency that "there are no formal proceedings going on against Mr Infantino".
The executive committee meeting took place in May at world football's governing body's congress in Mexico City, the first since Infantino replaced former president Sepp Blatter.
It included the resignation of Fifa's audit and compliance chief Domenico Scala, who claimed the new Fifa council would compromise the independence of key committees, including auditing, ethics and finance.
Fifa has denied reports that president Gianni Infantino is being investigated for a possible ethics violation.