It would also establish the post of a language commissioner, replacing the Welsh Language Board.
The 2011 measure wound up the former Welsh Language Board and created the office of commissioner.
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Ms Davies said the Welsh Language Board had been "very amenable" and had listened to concerns.
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John Walter Jones, chief executive of the Welsh Language Board until 2003, questioned the need for the role of language commissioner.
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However, Welsh Language Board members have written to Mr Morgan warning that any change to their organisation could damage the Welsh language.
The 2011 measure to promote the Welsh language saw the former Welsh Language Board wound up and the office of commissioner role created.
Concerns were also raised by a number of members that the Welsh Language Board would be scrapped as a result of the measure.
John Walter Jones, chief executive of the Welsh Language Board until 2003, questioned the need for the role of language commissioner at the time of the rejection of the standards.
Many businesses in Wales were using Welsh far more than they used to, and they were doing so in a spirit of goodwill with the support and encouragement of the Welsh Language Board, he added.
In July 2004, first minister Rhodri Morgan announced that most Welsh quangos will be abolished within two years and in November of that year said the Welsh Language Board would be added to that list and its duties and staff transferred to the control of the assembly government by 2007.
Set up in 1993 under the Welsh Language Act, the board's main aim has been to promote the use of the Welsh language.
Mr Andrews came under fire last summer when he ordered the WJEC board, which sets most of the GCSEs taken by Welsh pupils, to re-grade English language exams after the results were published.
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