The Irish Data Protection Commission (DPC) has met representatives from Twitter about concerns over the departures of a number of senior executives from the company.
Among those believed to have left Twitter is its Chief Privacy and Data Protection Officer, Irishman Damien Kieran.
One of the areas of concern for the DPC involves 'main establishment'.
Under data protection regulations, Twitter is 'main established' in Ireland, which means decisions about the processing of EU users' personal data are made here.
The US Federal Trade Commission said it was watching Twitter with "deep concern" after three privacy and compliance officers quit, resignations that could put Twitter at risk of violating regulatory orders.
Meanwhile, Twitter's new owner Elon Musk has said staff can work from home if it is not logistically possible to come into the office.
He was responding to a message on Twitter from an Irish-based worker who said they had been told to return to the office from tomorrow.
"Many of us work all around this country and are unable to do so," the worker wrote.
"This is in the middle of a housing crisis that Musk has absolutely no idea about, and it is almost impossible to move to Dublin so quickly.
"This is putting us under an intense amount of stress and uncertainty and, unfortunately, there is nothing we can do about it," the worker wrote.
Mr Musk replied that he was not ordering people back into the office.
"This is false," he wrote.
"Anyone who can be in office, should be. However, if not logistically possible or they have essential personal matters, then staying home is fine."
"Working remotely is also ok if their manager vouches for excellence," Mr Musk wrote.
On Thursday, Bloomberg reported that Mr Musk had emailed Twitter workers for the first time toprepare them for "difficult times ahead" and end remote working unless he personally approved it.
According to the report, the new rules were due to kick in immediately and would expect employees to be in the office for at least 40 hours per week.
