The modular accommodation would be used for patients who are mobile and need a short stay.
The HSE is considering setting up specially designed prefabs to relieve the trolley crisis.
A spokesman for the HSE told The Irish Independent that it will shortly evaluate a series of ids it received in response to a tender to provide the temporary accommodation within hospitals.
The Irish Nurses and Midwifes Organisation (INMO) reported 347 patients on trolleys across the country yesterday. In Fine Gael's election manifesto this year, Mr Varadkar spoke about introducing new trolley targets for hospitals whereby they will be required to improve on their numbers by 5% each year.
A spokesman said yesterday the pledged figure remained a target.
Prefabs would contain single en-suite rooms or four bedrooms, all of which would be fitted with standard bathrooms. The modular accommodation would be used for patients who are mobile and need a short stay. This could include patients with minor breaks, those waiting on tests results or those having a course of antibiotics.
Depending on the site, the prefabs could have between 10 and 60 beds. The units would be drawn on during periods of over-crowding in the worst-hit hospitals.
If the HSE decides to go ahead with the plan, staff would have to persuaded to work in the new buildings.
Yesterday, the worst hit hospital yesterday was in Tullamore, Co Offaly, where there were 28 patients waiting for a bed.