Anybody leaving the country currently has to have a “reasonable excuse” including medical treatment.
However, people do not currently have to prove to authorities that they attended medical appointments upon their return.
A spokesman for Mr Donnelly told the Irish Examiner: “The minister has asked officials to examine this issue.”
The Irish Examiner reports that senior gardaí informed the Department of Health about the issue at the beginning of February.
They were concerned the “reasonable excuse” proviso was being abused.
At the time gardaí and health chiefs discussed the issue, up to 50 people from Dublin had travelled to the Canary Islands for appointments at a dental practice, most of these people were in their 20s and 30s.
Staff at the Clinica Dental Tenerife Sur clinic later confirmed that the majority of these people did not turn up for their appointments.
Meanwhile, a number of the appointments were for non-urgent treatments including teeth cleaning and whitening.
One of the few permitted reasons for travel under Level 5 restrictions is for “essential medical, health or dental services”, or accompanying someone who needs essential treatment.
Those who are caught travelling without a valid reason can face fines of up to €2,000.
The Department of Health’s attempts to close the loophole have been hit with a number of legal issues including the EU Cross Border Directive, which includes rights for people looking to travel for medical treatment.