Twitter has told the Irish Data Protection Commission (DPC) that there are currently no changes to controllership or to its Irish board.
The DPC met Twitter's new acting Data Protection Officer this week to discuss concerns about the departures of senior executives from the company.
Meanwhile, Twitter's new owner Elon Musk has sent a message to staff telling them that they had until tomorrow to consider whether they wanted to stay on for "working long hours at high intensity" or take a severance package of three months' pay.
Among those who left recently was its Chief Privacy and Data Protection Officer, Irish man 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.
"On Monday, the DPC met with the new acting Data Protection Officer (DPO) of Twitter," a spokesperson for the Data Protection Commission said.
"He advised the DPC that there currently are no changes to controllership or to the Irish Board," the spokesperson said.
"Engagement with Twitter and the Office of the DPC is ongoing and expected to continue as the DPC monitors the situation," the spokesperson added.
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.
It comes as Mr Musk told Twitter employees that anyone who had not clicked on a link confirming "you want to be part of the new Twitter" by tomorrow would be considered to have quit.
"Whatever decision you make, thank you for your efforts to make Twitter successful," the message said.
Twitter did not immediately respond to a request for comment from Reuters.
"Going forward, to build a breakthrough Twitter 2.0 and succeed in an increasingly competitive world, we will need to be extremely hardcore," the message from Mr Musk said.
"This will mean long hours at high intensity. Only exceptional performance will constitute a passing grade."
Twitter laid off half of its workforce earlier this month shortly after Mr Musk took control of the social media company.
He has criticised Twitter's spending and work culture and said the company needs steep cost cuts and a reboot of its services.
Some Twitter employees who had criticised Elon Musk publicly tweeted earlier that they had been let go.
Additional reporting from Reuters