Mr Burgess paid for the Moet & Chandon Champagne and posted the photograph of the celebration on Twitter, which sparked the controversy.
The long-serving civil servant was appointed as Ireland's Ambassador to France and Monaco a year after the Covid rule-breaking party in June 2020. The Foreign Affairs Committee is due to meet today to discuss the ongoing controversy over the party.
It is expected Foreign Affairs Minister Simon Coveney and his current secretary general Joe Hackett will be called before a hearing.
Mr Hackett has been asked by Mr Coveney to compile a report on the party which will be presented to the minister before the end of the month.
Yesterday, Sinn Féin foreign affairs spokesperson John Brady said it would be "ultimately helpful" for Mr Burgess to come before the committee to answer questions.
Mr Brady said he wants to first see the details of the internal departmental investigation into the incident which saw around 20 civil servants huddled together drinking Champagne as they celebrated Ireland winning a seat on the UN Security Council.
"We are told it was an impromptu event," Mr Brady said. "If that's the case, how many bottles of Champagne does the department have lying around?
"If they were bought in, it would indicate it wasn't an impromptu gathering and was planned in advance. It would be ultimately helpful for the ambassador to come before the committee after we see the details of the investigations."
The department last week confirmed Mr Burgess paid for the Champagne out of his own pocket. Other committee members said their focus was on asking Mr Coveney to come before a hearing to discuss the Champagne party.
Fianna Fáil TD James Lawless, who also sits on the committee, said he didn't think people should be "hung, drawn and quartered" over the incident. He suggested it was being "exaggerated" by the opposition because of its similarities to Boris Johnson's travails in Britain, but in reality there was no comparison.
"I don't think it is comparable," he said.
He suggested on RTÉ Radio One that it had been "a momentary lapse of judgment", rather than a planned party to which invitations had been issued.
Meanwhile, it has emerged that Tánaiste Leo Varadkar knew a report into the Department of Foreign Affairs Champagne party was being considered when he called for the controversy to be investigated further.
During what is being described as a 'car crash' interview on RTÉ Radio One's This Week, Mr Varadkar suggested the party should be investigated when he was asked numerous questions about the long-running controversy.
However, the Fine Gael leader did not reveal that Mr Coveney had ordered his secretary general to launch an investigation into the Iveagh House party.
Mr Coveney also did not reveal details of the investigation when he appeared on RTÉ Radio One the day after he asked for the report to be compiled.
Mr Varadkar's spokesperson said: "The Tánaiste was aware that commissioning a report was under consideration but that a formal decision hadn't been announced yet, so he felt it better to leave the announcement to the Minister of Foreign Affairs."
Meanwhile, People Before Profit TD Paul Murphy has said that an "in-house review by a hand-selected civil servant" is not enough to address the breach of Covid-19 restrictions. The complaint was put to Mr Coveney's side for response.
Mr Murphy said: "We have seen how Boris Johnson has used a similar process in the UK to try dodge awkward questions. Now it seems the Irish Government is copying from his playbook."