Advertising revenue of £3m could be lost by some of Wales' biggest newspapers if the assembly government uses its own website to advertise jobs.
Mr Pugh said websites could be better used for job adverts
Culture Minister Alun Pugh warned Trinity Mirror - owners of the Western Mail and Daily Post - that the assembly may use its own website.
Mr Pugh said jobs adverts on websites could reach more people and save money.
Trinity Mirror said it was well placed to meet future challenges and said it offered value for money.
It is understood the assembly government currently pays around £3m a year to Trinity Mirror in advertising revenue.
Mr Pugh's was sacked as a Western Mail columnist in January after claiming opinion formers in Wales regarded the paper as "a bit of a joke".
He made his claim during an assembly culture committee review of newspapers in Wales which recommended that assembly advertising be split more evenly between papers.
The London-based Trinity Mirror group, owner of the Western Mail, Daily Post, South Wales Echo and two dozen other newspapers in Wales currently receives most money from the assembly for advertising.
Mr Pugh told BBC Wales News: "I certainly think in the longer term [Trinity Mirror has] got a serious challenge from new media.
The Western Mail is owned by Trinity Mirror
"For example both the assembly government and the public service more generally in Wales put a very substantial sum of money every year into the Trinity Mirror organisation for things like classified job advertising.
"At some point in the future there must be a tipping point whereas instead of paying very large sums of public money to Trinity Mirror to carry the job advertising it could be done for example... on the assembly government's own website."
He added the decision to move away from newspaper job adverts was not imminent.
"I'm certainly not saying we should do that now. What I am saying is that the media are evolving," he said.
"We've got an obligation to get the best value for public money."
A spokesman for the assembly government issued a clarification stressing that even if it moves towards internet-based advertising, it is likely it will still need to sign-post vacancies through newspaper advertising.
Trinity Mirror said it was "well placed to meet these challenges should they arise" as it is developing a portfolio of websites.
"Like any organisation with a substantial advertising budget, the Welsh assembly employs media planners and buyers to determine where that budget should be spent," said a spokesman.
"The Western Mail, along with newspapers in general, continues to offer both value for money and a huge audience - a fact recognised by the assembly."
A media expert warned that Mr Pugh was playing a "dangerous game" with the Welsh media.
Dr James Thomas from the Cardiff School of Journalism said: "The ability to hit the Western Mail's advertising revenue is one of the few hard weapons that the assembly actually has.
"There's always the chance that Trinity Mirror might reconsider the future of the Western Mail and might think with reduced revenue it's simply not worth continued investment.
"Ultimately it's a question of who needs the Western Mail most.
"Does Trinity Mirror need it or does the Welsh assembly and Welsh culture and politics need it?"