The 5,000 metres runner - who was included in Team GB's squad for the Olympics on Tuesday - suggested he had not followed protocols when he came back from a meet.
Butchart, speaking on an episode of the Sunday Plodcast which has now been deleted, said: "I'm not going to get in trouble from the police or anything like that.
"So you have to quickly, like, get an old PCR test, go on to Instagram, scribble out the time and the date, change the time and the date, and like change it so you can get into the country.
"Obviously Covid is huge, but it's quite annoying. Everybody has faked PCR tests, I'm sure, to try and go somewhere, because it's just so hard."
In a later statement to The Times the 29-year-old retracted his claims he had personally faked a Covid test but knew of athletes who had done.
"I have never falsified a PCR test and have always complied with the guidelines of the countries I have been travelling in," he said.
"The context of the podcast was about how hard it has been for athletes during the pandemic to travel and race, as you are depending on lots of factors that are out of your control.
But his actions will now be reviewed ahead of the Olympic Games, which start next month.
A statement from UK Athletics read: "UKA and the BOA (British Olympic Association) are aware of comments made as part of a podcast by a selected athlete today.
"Throughout the pandemic elite sport has been privileged to receive exemptions from various guidelines to enable athletes to continue to train and compete.
"We take very seriously any suggestion that an athlete has not followed these guidelines correctly and broken any COVID-related protocols.”
Reporting by PA