Campaigners said the move, a first for politics in the UK, would attract more women and disabled people to politics.
The Assembly Commission said job-sharing was a "possibility" under new powers.
The Electoral Commission said no joint candidacies were allowed in any UK elections under current law.
Sarah Rees, of the Women's Equality Party, said Wales should be the first to make the change, with the assembly encouraging flexible working by "leading by example".
The assembly will have powers to set its own elections, under changes being brought in under the 2017 Wales Act, which devolves more responsibilities from Westminster to Cardiff.
Currently 24 out of the 60 AMs in the Senedd are womeen, while no information is collected on how many AMs are classed as disabled.
In 2015, a bid by two Green Party activists to stand jointly for a parliamentary seat was refused and a bid for a judicial review was stopped by the High Court.
If they had been elected, the pair would have split the job 50/50 and have shared a vote in the Commons.
"I think Wales has got the power and I think it would be great for us to move forward and have shared candidacies," she said.
"You have people in very powerful positions able to do job shares, why can't we do it in government?
"It would give you the ability to have a very high-powered job and make decisions that reflect the society we live in, at the same time as looking after your family.
"If the Welsh Government can't do it themselves, why should any other business?