The Data Protection Commission is examining complaints it has received in relation to COVID-19 test results being made available to employers before staff members.
It centres on tests carried out at certain facilities.
According to the DPC, complaints have seen individuals 'expressing shock and upset' at receiving their results from managers rather than the HSE.
The DPC says says it's important these issues are clarified and rectified - noting that it appears that, at a minimum, "communication has been unclear to the affected staff members in terms of how the process is being managed".
Deputy Commissioner Graham Doyle says it would be expected staff would learn of the test results before management.
He explained: "We cannot see how it would be legitimatised that medical test results of this nature would be not communicated in the first instance directly to each individual staff member - whether that's via text message or a phone call notifying them of the result.
"While it may be necessary for the HSE to inform management and employers of positive results after the staff member has received those results in the context of the tracing of close contacts in the aggregate setting, this does not negate the need to communicate with the individual about their personal data."
Meanwhile, it has emerged at the COVID-19 Dáil Committee that public health officials are allowed the discretion to tell employers about a positive coronavirus test before they inform staff.
When there are mass screenings of workers - such as in factories - the results have sometimes been given to the employer before being given to the people actually tested.
Chief Medical Officer Dr Tony Holohan has said such cases would be a breach of confidentiality.
HSE boss Paul Reid acknowledged it has happened.
He said: "In relation to some of the employers that we've been proactively testing over the last few weeks, there is a responsibility on the public health official to get those results out urgency.
"There may have been a case - probably one case that we know of - where it was notified to the employer [of] a significant number of positive cases. That discretion is for the public health official to make."