Property investors could lose capital gains tax concessions as the Turnbull government looks at ways of improving housing affordability and its own budget bottom line.

Options being worked through include following Labor in halving the 50 per cent discount on capital gains tax to 25 per cent or reducing it by another amount, the Australian Financial Review reported on Thursday.

Another option is adopting a phased model in which the discount would increase the longer the property was held.

A property would have to be held for several years before the investor was eligible for the full 50 per cent discount.

As it stands now, the discount applies as long as the investor holds the asset for a minimum of 12 months.

Treasurer Scott Morrison insists he has “absolutely no desire whatsoever” to raise taxes, but the government is facing the double-whammy of falling revenue and increasing spending as it prepares the May budget.

“We will exhaust every option we have to deal with the expenditure problem we have. Once that is done, the budget will then be framed,” he told Fairfax Media

Asked directly if that meant a tax rise was on the cards, he said: “The menu of options is well known.”

Minister for Education and Training Simon Birmingham refused to comment on speculation about changes to capital gains tax concessions, saying it wasn’t his portfolio.

We’re still months away from the budget but our government doesn’t want to see tax go up,” he told ABC radio.

“Our view is we should be able to prioritise spending in Australia where we need it.”

Senator Birmingham said the government was not looking at tax increases “at the present”.