A total of 24 people have received letters asking them to attend interviews in respect of the funeral of IRA man Bobby Storey in June, the PSNI chief constable has revealed.
Simon Byrne said the investigation into potential breaches of social distancing rules should be completed within the next number of weeks.
He appeared before Stormont's justice committee on Thursday.
Deputy First Minister Michele O'Neill was among those contacted.
Her Sinn Féin colleague Linda Dillon, a member of the committee, said she was another of those who received a letter after attending the funeral.
She said she was there for "the funeral of a very close friend of my family for over 20 years".
There has been criticism that the large gathering at the funeral was in contravention of the NI Executive's coronavirus guidelines.
Ms Dillon told members that rules were broken at many funerals and said "the blatant hypocrisy in this room would actually sicken you".
Earlier this month, Deputy First Minister Michelle O'Neill conceded that the executive's public health messaging had been "undermined" by what happened.
The investigation is being led by Mark Webster, the deputy chief constable of Cumbria Police.
Simon Byrne said the inquiry is "reviewing different types of footage to see where there are potential breaches to regulations at a number of different places".
"Twenty-four people have now received letters inviting them to make arrangements for interview with us in the next 14 days, well the clock's ticking, it's probably about the next seven now," he confirmed.
The chief constable's comments followed a request for an update on the investigation from Ulster Unionist MLA Doug Beattie.
During the remarks, committee chair Paul Givan asked "is it likely" that a report will be sent to the public prosecution service.
Mr Byrne replied: "The way the law works here, there has to be."
Linda Dillon asked the chief constable if other funerals faced the same level of investigation.
He said there were 20 investigations into other funerals during "the Covid period" and 13 of them have already closed "in terms of the fleeting nature of the breach".
However, he said he believed from memory that six funerals are currently under investigation.