The pair have impressed United manager Martin Foyle, who has issued an urgent appeal for the county’s business community to save the youth set-up.
The youth team set-up will be disbanded at the end of the season unless the club can secure in excess of £65,000 funding by next week.
Murphy is a product of Leominster Minors and has been on the bench for the first-team, while Williams has made a brief substitute appearance against Nuneaton.
“Cory and Bill have got something about them about but they have a long way to go in terms of making the step up to men’s football,” said Foyle.
“The two have not yet started their careers and there’s a big step up between youth and senior football. But they are off to a good start.
“They both got good composure on the ball and that’s the type of level of player which we can afford next year.”
United’s youth team, managed by Peter Beadle, reached the fourth round of the FA Youth Cup before bowing out to Manchester City after extra-time.
And if United’s board are not in advanced negotiations with a potential sponsor by February 17, United’s youth set-up will be discontinued next season.
Foyle said: “Since I have been at the club there has been a lot of talk of people putting money in, people are going to do this and they’re going to do that, but it hasn’t materialised.
“A youth set-up is very important to a club like Hereford United.
“Perhaps the sponsorship money for the youth set-up could be financed by a group of people or several businesses.
“And if people want to, the money could be put into the club and ring fenced for the youth set-up if they are not happy putting money directly into the club.”
Foyle added: “We are looking at all of the youth team but, at the moment, we don’t know the budget we will be working with for next season.”