George Peat stated that he heard a section of the Rangers supporters singing this song during Saturday's match against Hamilton. Mr Peat said he would be meeting with officials of the Scottish Premier league and the police to plan a way forward on this issue.
"At the minute, we've left it in the hands of the SPL to look into things and try to eradicate it," he told BBC Sport.
"Obviously, it's got to be stamped out and we'll be having a meeting soon with the SPL and the police to see what we can do about it."
Mr Peat's comments come only a few days after Fine Gael TD Joe McHugh called Minister for Foreign Affairs Micheál Martin to write to Scottish First Minister Alex Salmond about the song and, in particular, the racist abuse directed at Hamilton and Ireland footballer James McCarthy.
"I have asked the Minister for Foreign Affairs to request that the Scottish authorities take action against those Glasgow Rangers supporters who sing the song.
"The racist abuse to which James McCarthy is being subjected on the terraces at some SPL venues this season because of his declaration for Ireland is hurtful for James's family and is offensive to this country. I have contacted the Minister for Foreign Affairs requesting that he write to Scotland's first minister and to the Scottish Football Association in relation to this matter.
On Saturday Rangers fans at New Douglas Park amended the famine song to sing: "James McCarthy, why don't you go home?"
Two weeks ago SFA CEO Gordon Smith stated at an anti-racist event in Edinburgh: "The lad [McCarthy] has made his decision to play for Ireland. It was his decision to make. People should leave the kid alone."