The pair will miss Sunday's final Pool D game against Uruguay at Kumamoto Stadium after suffering injuries in the bruising victory over Fiji on Wednesday.
Fly-half Biggar is undergoing head injury assessment (HIA) protocols for the second time at the tournament after a collision with team-mate Liam Williams, while centre Davies sustained a knee injury.
"Dan's said he feels really good in himself. He's come through symptom-free and he's going through the HIA protocol at the moment," Gatland, pictured, said.
"Hopefully Jonathan will be OK. The knee was pretty good the next day. It had a little bit of swelling, so he's been icing it regularly. He gets a bit more time so hopefully that keeps improving over the next few days."
Gatland has made 13 changes for the game against Uruguay and admitted naming the XV had been a juggling act given the four-day turnaround and having taken only 13 backs to Japan.
Winger Josh Adams, the joint top try-scorer in the tournament with four, would likely have been rested this weekend but will play. Centre Hadleigh Parkes is the only other player retained from the bruising encounter with Fiji.
Scrum-halves Gareth Davies and Tomos Williams have both been named on the bench as they can slot into other positions.
Wales will seal top spot in the pool with victory - two losing bonus points would also be enough - and set-up a quarter-final against France at Oita Stadium on Sunday 20 October.
Gatland has told players who will be making their tournament bows on Sunday that they can still force themselves into his plans for the knockout stages.
"It's been a bit of a juggling act with the four-day turnaround," the New Zealander said. "We knew from the start that we were going to expose a few players.
"The message to the players against Uruguay is that the door is not shut. There are opportunities... to stake a claim for a quarter-final spot.
"We've got to start well. It's Uruguay's last game and they'll want to finish on a high. We need a good performance and particularly up front. We want to get the job done, then we can focus on the quarter-finals."
Wales look likely to face a France side who will have had two weeks to prepare for the game after their match against England was called off, while Gatland's team will have played twice in that period.
"That's going to be an interesting dilemma for them and what they do in the next few days, in terms of preparation," Gatland said. "Some teams will welcome it because it gives them an opportunity to freshen up and get back on the training pitch.
"For us, it's about continuing the momentum and building on that. Hopefully after Sunday we can start thinking about getting down to Oita and preparing for a Sunday game against France.
"They would be very tough but we have to do a job against Uruguay first and we must make sure we get that win. Otherwise, it's England."