The complaint was made after Rangers' victory over Celtic last month
Irish diplomats have raised concerns with the Scottish Government over chanting by a section of the Rangers support at last month's Old Firm match.
Representations were made by Ireland's Consul General after a Celtic supporter complained about a song which refers to the Irish potato famine.
Rangers FC said it has asked its fans to refrain from singing the song.
The Scottish Government confirmed it had been advised by Ireland's Consul General of the Celtic fan's complaint.
The controversy surrounds a song which referred to the famine which killed an estimated one million people in the 1840s and set in motion the mass migration of Irish people.
The song includes the line: "The famine's over, why don't you go home?"
After the song was sung by some Rangers supporters at August's Old Firm game, a Celtic fan wrote to the Irish Embassy in London to complain.
The Irish consul general in Edinburgh raised the issue at her regular meeting with the Scottish Government.
The Scottish Government made no comment on the discussions, but insisted that several campaigns against bigotry were beginning to work.
A spokesman said: "The Scottish Government is totally committed to combating sectarianism and bigotry, which is why we have expanded on the work of the previous administration and are doing more.
"We are working with the clubs themselves, as they are part of the solution to the problem."
A spokesperson for Rangers said: "In the days following the recent Old Firm match, the club were made aware that a substantial number of complaints had been made regarding the singing of the chorus of a song known as 'The Famine Song' by our supporters at this match.
"Rangers Football Club approached Strathclyde Police for guidance on this matter, with a view to issuing a joint statement indicating that persons singing this song in future may face the possibility of arrest.
"Strathclyde Police were not able to commit to this until they had carried out further investigation."
The spokesman said the club had a long-established policy of encouraging sporting behaviour and discouraged the singing of songs which others found offensive.
"Clearly 'The Famine Song' has provoked such a response in certain quarters," he added.
"It is the club's view that the interest of our supporters and the club will be best served by supporters refraining from singing 'The Famine Song'."