Visas giving the right to settle in Britain could be auctioned off to the highest bidders under proposals expected to be unveiled on Tuesday by the government's official immigration advisers.

The suggestion, expected from the home secretary's migration advisory committee (Mac), has already been criticised by immigration lawyers for creating an "eBay culture" for permanent UK residence.

Under the proposal overseas millionaires will be invited to bid for a limited proportion of investor or tier-one UK visas which allow holders and their families to live indefinitely in Britain.

A second option would allow visas to be "bought" through donations to hospitals or universities.

The proposals are expected to be put forward in response to concerns that the existing investor visa route is failing to benefit the UK and has simply become a cheap way for some wealthy Russian, Chinese and Middle Eastern families to settle permanently in Britain.

The existing route, known as tier one of the points-based immigration system, lets rich individuals accelerate the process of being allowed to settle in the UK by between two and five years depending on how much is invested.

Applications have been running at about 600 a year to apply under this route which does not require applicants to be able to speak English or have a job to come to.

Official concern over the use being made of tier-one visas first came to light in December 2012 when the Home Office announced that leveraged investment funds held in offshore accounts could not be used to fund their investments in Britain.

There has also been concern that the investments have been made have often been in government gilts or loans to the applicant's own businesses – neither of which are directly beneficial to the British economy.

Professor Sir David Metcalf, chairman of the migration advisory committee, has told MPs he thinks it is time to think more creatively about the operation of the investor visa route. "It may very well be that we should be auctioning some of these slots," he told the Commons home affairs select committee. "There should be a proper discussion about it. Equally it may well be that we should be letting people in if they endow a Cambridge college, a major teaching hospital or the London School of Economics with £10m," he added.

Nick Rollason, head of business immigration at the Kingsley Napley law firm has warned that an auction of investors' visas would create an "eBay culture" for visas that would leave a bad taste in the mouth of the British public.

Another leading immigration lawyer, Sophie Barrett-Brown of Laura Devine Solicitors, added: "An auction approach has, rightly, been rejected by the Home Office previously (when the points-based system was first introduced) and sent out the wrong message to the public."

She said that the alternative suggestions expected in the Mac report had to be seen in the context that it had been asked to provide an analysis and recommendations on the economic impact of tier-one investors: "The UK government will take into account wider policy considerations in deciding which of the migration advisory committee's suggestions to follow," she said.