The proposals are to change the foundation phase of both schools to Welsh language education from September, 2022. This would only affect pupils starting in the foundation phase, and pupils currently attending the school would be unaffected.
Councillors on a scrutiny committee approved the recommendations going before the executive board at a meeting on January 28, having raised questions about the consultation process and also the potential impact on pupil numbers at Ysgol Y Felin.
The meeting also heard that some Model Church in Wales governors weren't aware of the proposal, although council officers had already talked it through with the governing chairman and head teacher.
Officers were due to meet with school representatives on Tuesday, February 2, and feedback will be considered by executive board members six days later.
The English language school is funded but not owned by the council and had 429 pupils - including nursery - as of January last year. It is the former school of First Minister Mark Drakeford.