The Welsh Government wants to give the National Assembly for Wales a new bilingual name instead of a Welsh-only moniker, BBC Wales understands.
It comes before AMs vote on a bill to change the institution's name to the "Senedd".
Former first minister Carwyn Jones has tabled an amendment to the bill - favouring a bilingual name - "Senedd Cymru" and "Welsh Parliament".
He told Newyddion 9 the Welsh Government supports his amendment.
A Welsh Government spokesman said: "The government regularly works with backbenchers to bring forward amendments to improve legislation."
The vote is due to take place on 9 October.
Carwyn Jones said a bilingual name should be given to the legislature "at least" on a temporary basis, so everyone understands what the institution does.
Andrew RT Davies is another AM who opposes a Welsh-only name.
"There's always discussions going on where common ground can be found because, to get an amendment through, you have to have a majority vote," he said.
"I believe such discussions are being undertaken. This shouldn't be a controversial choice, this is ultimately, respecting the legislation that's in place to protect both the Welsh language and the English language.
"This is a parliament - senedd - both words are perfectly acceptable in most people's minds here in Wales."
AMs agreed the General Principles of the Senedd and Elections (Wales) Bill in July.
There were 42 for, no abstentions and nine against.
It is understood the First Minister, Mark Drakeford, told Cymdeithas yr Iaith Gymraeg, he favours a Welsh-only name.
Plaid Cymru also wants a Welsh-only name as the Welsh language "belongs to all people in Wales."
An Assembly Commission spokesman said Presiding Officer Elin Jones supports a Welsh-only name too.
Cymdeithas yr Iaith said: "It's a definite concern that a number of the arguments used against a Welsh-only name are patronising to the hundreds of thousands of people in Wales who support the language but cannot speak it.
"Many people already call the institution the 'Senedd' - just as they proudly sing the Welsh words of our national anthem. Everyone, from every background, has the right to celebrate the uniquely Welsh things, and no-one has the right to tell non-Welsh speakers otherwise.
"By giving the Senedd an English name too, it will inevitably normalise that name and undermine the use of the Welsh name."