Warren Gatland says Wales' focus is on "competition rugby" as they continue counting down to their World Cup opener against Georgia.
Beard is recovering from having his appendix removed and hopes to join the squad in Japan next week, while Hill is continuing rehabilitation following a stress fracture in his leg.
A pivotal Pool D clash against Australia six days after the Georgia game is the likely target for both players.
"We've picked up a couple of injuries and there is a concern at the moment with the second rows," Wales head coach Warren Gatland told reporters at the squad's base in Kitakyushu.
"He (Beard) is hoping to come out on Thursday and probably not going to be available for selection for the Georgia game.
"But we are hopeful – and the medics are confident – that he will be available for selection for the Australia game."
It suggests that Jake Ball will be skipper Alun Wyn Jones' second-row partner for the Georgia game, with flanker Aaron Shingler providing lock bench cover.
On Hill, Gatland added: "(The medics) are confident that he will be available for selection against Australia.
"He's been out of his boot and on the training field today, even though he wasn't doing any running.
"Hopefully, after that Georgia game he will be back training and available for selection."
The Wales squad are enjoying temperatures of around 30 degrees and unbroken sunshine in the southern Japanese city, where they will be based until Thursday.
They have also received a warm welcome, with hundreds of schoolchildren greeting their arrival at the airport, while banners and flags of support are draped all over the city.
Wales lost three of their four World Cup warm-up games during the past month, but those results will have little relevance when it comes to tournament business in Japan.
"We haven't shown much in our play so far – we've played differently as well – but now the focus is really on competition rugby," Gatland said.
"We feel that it's important to get off to a good start, and if we do that, hopefully we can qualify for the quarter-finals out of this group.
"It's going to be tough for us, but if we do that it's then one game at a time.
"There is a lot of confidence and self-belief in this side that if we play to our potential we can go a long way in this tournament."
Fly-half Rhys Patchell, meanwhile, has done some non-contact work after suffering concussion during Wales' final World Cup warm-up game against Ireland eight days ago.
"He has gone through the HIA (head injury assessment) protocols," Gatland added.
"He was training this morning, just doing some non-contact stuff at this stage.
"We will ease him back into contact work later in the week, making sure that we go through the protocols and ensure he's 100 per cent and available for selection."