The Women in Democracy Caucus also wants extra support for women AMs, and more women experts on TV and radio.
Its leader - Presiding Officer Rosemary Butler - said women's voices were "not being heard".
The Welsh government said banning companies from procurement processes would be illegal.
However, a spokesman added: "While we have to recognise this legal constraint, no-one should be in any doubt regarding our dedication to maximising women's participation in all areas of public life."
The report was produced to coincide with International Women's Day.
Dame Rosemary said: "Women's voices are not being heard and our views are being overlooked, so I am working to address the need for more women to apply for and take up public roles and appointments."

The car was bought by Rick Champagne, a logistics company owner from Phoenix, Arizona.
The 56-year-old, who was just 10 when the high-camp TV series began in 1966, said it "was a dream come true".
The Batmobile design was based on a 1955 Lincoln Futura, a concept car built in Italy by the Ford Motor Company.
It was the first time that car had come up for public sale since it was bought in 1965 by car-customiser George Barris for a nominal fee of $1.
Barris then spent $15,000 (roughly £5,370 at the time) to transform it into the famous superhero vehicle, over a period of 15 days.
It had a V-8 engine,  arguably one of the first in-car phones, and parachutes, which were deployed to help Batman turn sharp corners.
Mr Barris told reporters at the auction: "The car had to be a star on its own. And it became one."
Since the show was cancelled in 1968, he  has toured the Batmobile and was eventually housed in a private showroom in California.
Adam West,  now 84, played the caped crusader in 120 episodes in four years of programming, with Burt Ward starring as the "boy wonder" Robin and comedian and actor Cesar Romero as Batman's arch nemesis, The Joker.
The 60s show was camp in its portrayal of Batman. More recent incarnations of billionaire Bruce Wayne and his alter-ego - such as British director Christopher Nolan's Dark Knight trilogy  - have had a much darker tone.
The newer Batmobiles have reflected the more brutal portrayal of Gotham City's saviour, such as the "Tumbler" of 2005's Batman Begins, starring Christian Bale.

The 10-part Channel 4 and Sony Pictures Television series, based on Dick's short stories, will star Breaking Bad's Bryan Cranston.
Other writers on the project include Matthew Graham (Doctor Who) and 50 Shades screenwriter Kelly Marcel.
Filming is expected to begin early next year.
Fear and Loathing in Las Vegas writer Tony Grisoni is also one of the scriptwriters on board.
The new writers were revealed at a dinner ahead of the Edinburgh International Television Festival.
Each episode of Electric Dreams will be a standalone piece, adapted by a team of authors which also includes Masters of Sex's Michael Dinner and Outlander's Ronald D Moore.
Dick, who died in 1982 at the age of 53, had 44 novels published. His first was Solar Lottery in 1955.
He is best known for works including The Man in the High Castle and Do Androids Dream of Electric Sheep? - the basis of 1982 film Blade Runner.
Other films based on Dick's books include Total Recall and Minority Report. He also wrote more than 100 short stories.
Harry Potter and the Cursed Child, the West End stage play written by Thorne, is set 19 years after the seventh and final book in the series by JK Rowling.
Presented in two parts and running to more than five hours, it shows the main characters from the books as adults in their mid-30s as their own children head off to Hogwarts.
Demand for tickets for the two-part show has been huge. The show is sold out, although there is an online lottery every Friday in which 40 tickets are released for every performance the following week.
Thorne's other TV credits include two Bafta-winning series, This is England and The Fades.
Follow us on Twitter @BBCNewsEnts, on Instagram, or if you have a story suggestion email entertainment.news@bbc.co.uk.
Organisations without women on their boards should not be given Welsh government grants or contracts worth over £250,000, a group of AMs has said.
[NEXT_CONCEPT]
The Batmobile used by actor Adam West in the original TV series of Batman has sold for $4.2m (£2.6m) at a US auction.
[NEXT_CONCEPT]
Harry Potter and the Cursed Child writer Jack Thorne is joining new TV drama Electric Dreams: The World of Philip K Dick.