Markos Kyprianou is due to launch a debate at the European Commission on the issue later.
The Financial Times reports he wants patients to have the right to care in any of the 25 member countries.
About 1% of operations carried out across the EU involve people who come from other countries. However, health tourism is on the rise, with people going abroad for treatments ranging from IVF to cosmetic surgery.
Many EU members have argued that medical services fall outside the scope of the single market.
But the European Court of Justice ruled in May, in the case of British woman Yvonne Watts, that patients facing "undue delays" in their waits for operations should be entitled to have treatment in other EU countries.
Mrs Watts went to France for a hip operation because she faced a year-long wait for an NHS procedure.
Mr Kyprianou told the newspaper: "The internal market applies to health services. People can shop around.
"We need to give people more information.
"For example, if you want a hip replacement, where do you go, which country?
"There must be a better way to help the citizen make a choice."
But he added: "On the other hand, can a receiving country turn down a patient?"
Mr Kyprianou said that the issues of who should be liable if something goes wrong and who should pay for follow-up treatment had to be discussed.
The commission's debate on Tuesday will look at proposals for how an EU health market would function.
Mr Kyprianou's suggestion is that patients would only be able to travel for treatment that would be available in their home country at the same price.
They would have to pay any extra costs themselves.
However, the move could have significant implications for health services such as the NHS, which has a limited capacity and long waiting lists.
A spokesman for the Department of Health said: "We are talking about a very small number of people.
"Last year the number of UK citizens who travelled abroad specifically for treatment was just 230 - compared to 1,100 in 2000.
"This drop is in part due to a successful reduction in waiting times, plus the preference most patients have for treatment closer to home."
He added: "In a small number of cases patients in the UK are entitled to travel abroad for treatment following consultation with their doctor.
"We welcome the European Commission's intention to consult on this sensitive area of healthcare."