The move would also ease the "growing burden" on politicians in Cardiff Bay as more power is devolved, the group's Wales director Martin Warren said.
Peers serving in the UK cabinet have set the precedent, he added.
Parties in the assembly have questioned the idea on the grounds of democracy and accountability.
The accountants' organisation said scrutiny of Welsh legislation was suffering due to "significant workloads for politicians shifting from Westminster to Cardiff Bay".
If it proved difficult to increase the number of AMs from the present 60, a bigger role could be given to the 40 MPs from Wales as their role in Parliament diminished, Mr Warren said.
He suggested letting the first minister appoint MPs to the Welsh cabinet, or inviting MPs to serve on assembly committees, in both cases reducing the demands on the time of politicians in Cardiff Bay.
Another idea put forward was the creation of a non-political body of professionals who could advise on and scrutinise policy.
"Wales is a small country with limited resources and making best use of those resources within a democratic framework to achieve for Wales must surely be an objective that crosses all political borders," said Mr Warren.
Dr Rebecca Rumbul, politics lecturer at the Centre for Lifelong Learning at Cardiff University, said involving MPs in assembly business might be "confusing" to voters.
Liberal Democrat AM Peter Black was also doubtful, claiming MPs "won't be able to do either job properly".
Welsh Conservative leader Andrew RT Davies said: "After 17 years of the same old, tired ideas in a Labour-run Wales, our country needs a change.
"May's election is the chance to choose the Welsh Conservatives and secure new ministers, fresh ideas and a brighter future."
For Plaid Cymru, former presiding officer Lord Elis-Thomas said it was "a completely anti-democratic idea".
"The notion that people could come down to Cardiff, turn up and be ministers without having been elected takes us back to a pre-democratic period, and certainly before the assembly was in existence," he told BBC Radio Cymru.
"If anyone is suggesting something like this, we'd need to have a referendum immediately."
A Welsh government spokesman said: "Ministers are selected from the membership of the democratically elected National Assembly and we see no need to change this."

Real scored three goals in the first 16 minutes, with Karim Benzema heading the first from a James Rodriguez cross.
Ronaldo then added a penalty before Rodriguez scored with a deflected shot.
Ronaldo made it 4-0 by half-time with a fizzing effort before completing his hat-trick with a header, which was followed by a Oscar Duarte own goal.
With Rodriguez filling in for the injured Gareth Bale in Real's front three, Espanyol were ripped apart.
Ronaldo was the star as he moved level with Barcelona's Luis Suarez - on 19 goals - in the race to be La Liga's leading scorer.
It was a testing debut for Espanyol's new goalkeeper Giedrius Arlauskis, signed on loan from Watford during the week.
The Lithuania international faced England in a Euro 2016 qualifier in October, but his only previous start at club level this season was for the Hornets in a Capital One Cup defeat at Preston in August.
Arlauskis saved well from Ronaldo's early free-kick and could not be blamed for Real's three quick goals.
He also got a hand to Ronaldo's shot for his second goal, but the Portugal international's dazzling footwork deserved reward as he bamboozled the visiting defence to create space to score.
The goal rout ended when Costa Rica international Duarte turned Jese's low cross into his own net.
Both teams are in La Liga action next Sunday, with Real Madrid visiting relegation-threatened Granada, while Espanyol host Real Sociedad.
MPs could serve as Welsh government ministers in a bid to widen the talent pool, the Institute of Chartered Accountants in England and Wales says.
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Cristiano Ronaldo scored a hat-trick as Real Madrid thrashed Espanyol to cut the gap between themselves and La Liga leaders Barcelona to four points.