The Danish ambassador was "caught a little off guard" and the conversation "moved on," the senator's spokeswoman, Caroline Tabler, told the outlet.
Cotton also reportedly discussed the potential purchase with Trump last year, but, according to the spokeswoman, the two had not discussed the matter since.
Last week, media reported that US President Donald Trump was considering buying the world’s largest island Greenland, which is an autonomous region within the Kingdom of Denmark. A few days later, Trump confirmed the reports, adding though that he wasn't thinking about the purchase as a pressing issue.
After Danish Prime Minister Mette Frederiksen rejected the idea, Trump cancelled a visit to Denmark.