The Assembly Commission, which runs the institution, said the case for more AMs was "more compelling than ever".
Currently there are 60 AMs but there have been longstanding calls from political parties for more members to deal with the assembly's workload.
A previous report said that increasing the number of AMs from 60 to 80 would cost up to Â£9m in the first year.
The commission over sees the operation of the Cardiff Bay legislature - it is made up of politicians from all four party groups and the presiding officer.
As well as the number of members, the commission is also considering whether the assembly needs a new office block.
Ms Jones, who is AM for Ceredigion, said: "The commission is taking the decisions necessary to make our parliament fit for the future - giving young people a voice in our democracy, communicating effectively with the public and fulfilling its statutory duty to enable the assembly to undertake its legislative and scrutiny work.
"Repeated examination of the capacity of the assembly has demonstrated that it is under-powered and over-stretched given the scale of its law making and fiscal powers.
"The scale of the challenges we face mean that the Commission must have the courage to take decisive action.
"Should the Wales Bill pass, and the assembly decide to exercise its new legislative powers in this area, we are determined to do what is necessary to equip our parliament with the capacity to deliver a strong and sustainable Welsh democracy."
The commission agreed that the case for a larger institution was "more compelling than ever", and agreed to explore the issues further, "drawing on neutral, expert advice".
Powers which could allow for changes to the number of AMs will be devolved to the assembly subject to the passage of the Wales Bill.
A Plaid Cymru spokeswoman said her party had "long called for the Assembly's capacity to be increased".
"This would provide more opportunities to hold the Welsh Government to account and ensure that they deliver on their promises to the people of Wales," she said.
The Welsh Assembly is "over-stretched" and needs more members, Presiding Officer Elin Jones has said.