BBC Wales understands an advisory panel on creative industries recommends rejecting a request from University of Wales Trinity St David for up to £6m.
The panel is concerned a similar hub already exists in Swansea.
Camarthenshire council leader Emlyn Dole said the comparison was "completely inappropriate".
The panel is chaired by Ron Jones, executive chairman of Tinopolis.
It did not take into account whether the scheme - Yr Egin - would provide any educational or linguistic benefits.
Economy Secretary Ken Skates told the assembly in November it was "disappointing" that a "funding gap" had appeared since the university first announced the plans in 2014.
Mr Skates has yet to decide on the university's application for between £4m and £6m of public funding.
Directors of the project have previously estimated the new centre for creative industries would be worth £11m a year to the local economy.
Planning permission for the development was granted in October and Kier Group has been appointed as the main contractor.
S4C has previously said its plans to relocate remain unaffected, with 55 jobs moving from Cardiff.  It has agreed to pay £3m in upfront rent for a 20 year lease.
The Welsh Government, the university and S4C have refused to comment.
Carmarthenshire council leader Emlyn Dole said he was extremely disappointed and concerned by the news.
"The comparison between the development in Swansea and Yr Egin is completely inappropriate," he said.
"Yr Egin involves the construction of a pioneering creative and digital hub and the development of a creative sector cluster, not just for the Swansea Bay region but for the whole of Wales."
Plaid Cymru economy spokesman Adam Price claimed "continued speculation" over the future of Yr Egin could put the wider £1.3bn "city deal" investment plan for the Swansea Bay region at risk.
"This project poses no financial risk whatsoever to the Welsh Government," he said of Yr Egin.
"The university has presented a series of funding proposals which would see the taxpayer fully reimbursed if the project doesn't meet the performance criteria agreed.
"So, with the university acting as a guarantor for the investment, we have to ask the Welsh Government: what's stopping you?"
A creative industries development in Carmarthen which includes the new headquarters of S4C should not receive public money, ministers have been told.