"The last time around they succeeded in more or less keeping the budget constant in nominal terms, but this time around it will be harder to repeat. The reality is there will probably be less money."
Prof Matthews said the UK's decision to leave the EU compounds these concerns.
The current CAP runs up to 2020 - the end of the bloc's long-term budget. It is worth around €56bn a year to farmers across all member states. Ireland gets around €1.5bn.
However, by the time the current CAP runs out, the UK will have left the EU, leaving less cash in the bloc's coffers.
"Brexit is potentially a hammer blow for Irish agriculture. If Brexit occurs over the next couple of years, before the next CAP comes into force, that will also mean there is less money in the kitty, the UK is such a big net contributor. So I think that is another reason to expect that the money will be lower," Prof Matthews added.
Speaking at last month's Agricultural Conference in Brussels, Phil Hogan, Agriculture Commissioner, who will publish a paper on how to simplify and modernise the CAP this year, highlighted the need to "reconsider the effectiveness" of the toolkit available.
He raised questions on whether existing tools intervene sufficiently and quickly enough at times of crisis and suggested that farmers should have "greater built-in measures" to help in difficult times on the basis of a risk management.
"It is my determination that basic income support and an effective safety net will continue as an essential element of any new CAP through a system of direct payments," he said.
However, he also warned farmers that "the new CAP will have to have a higher level of environmental ambition" than before in order to help the bloc meet its more stringent 2030 climate targets.
"Our farmers and related actors will have to focus on the challenge and innovate as never before," Hogan said.
"When they [farmers] start to lead from the front in terms of sustainable intensification, they will be delivering products of the highest quality with impeccable environmental credentials.
"That's what the market wants."
Prof Matthews anticipates that any new environmental objectives will be tackled through changes to the second pillar of CAP. However, that would ultimately mean less money would be available in Pillar I.
"There may be some further incentives in the Pillar II rural development side of things because I can't really see how you can use Pillar I payment to target climate on a per hectare basis, they are not very targeted to a specific objective.
"If there is less money, and we stick with the two pillar structure of the CAP, the big decision presumably will be should we try to protect Pillar I, the direct payment, at the expense of heavier cuts in Pillar II? Or should it go the other way around to maintain the Pillar II-type schemes at the expense of less money for Pillar I?" he asked.
"If we take the commissioner seriously on the environmental issues and sustainability issues, his instinct might be to protect the Pillar II budget."
Prof Matthews said such a move would rankle with many farmers.
"There will be winners and losers. Obviously existing farmers are going to scream. But I think for new farmers who are coming in, they will be able to access land more cheaply. I think probably it's not going to affect them.
"If payments come down, lands gets cheaper and farmers who use rented land will actually be able to get land cheaper," he said.