VHI and Laya have ruled out price hikes in the wake of Aviva plans to push up its premiums in July.
But there was no comment from GloHealth, prompting experts to speculate that it is planning price rises.
State-owned VHI said it had no plans for any price increases.
Laya Healthcare, which is the second largest in the market, said it "has no plans currently to increase premiums across our schemes".
GloHealth, the smallest player in the market, did not provide a response.
Aviva is increasing its premium rates by an average of 5.5pc, with some plans rising by 15pc.
The insurer blames the rise on its increased cost of claims. The increases will come into effect from 1 July.
The move is despite expectations that the enormous rise in customers in the past month would put pressure on insurers to avoid inflating premiums.
In April, 74,000 people took out health insurance in order to avoid penalties on over-34s.
The surge in customers has reversed the decline of recent years to the point where 2.1 million people now have health insurance cover.
But health insurance expert Dermot Goode said he expects GloHealth to follow Aviva with price rises.
"I expect price movement on some Glo plans, but there is no detail available yet," Mr Goode of Totalhealthcover.ie said.
Aviva has blamed the increased cost of claims and an ageing customer base for the price hikes. The hikes will affect more than 100 different plans.
The increases will mean some plans rising by between €200 and €470 a year for families.
The Aviva price rise comes just a month after there was a surge of new entrants into the health insurance market.
Consumer advocates had argued that the larger-than-expected numbers who took out cover last month would put huge pressure on insurers to avoid premium hikes.
Life-time community rating came into effect at the start of this month, with penalties being imposed on the over 35s who take out cover for the first time.