Cardiff number eight Faletau was unavailable to face France because of a knee issue.
The 34-year-old has played 104 internationals for Wales and five Tests for the British and Irish Lions.
Faletau has not been involved in an international since the World Cup pool victory against Georgia in October 2023 because of a series of injuries.
That was the last time Wales won a Test match with Gatland’s side having since suffered 13 successive international defeats, including seven Six Nations losses on the bounce.
Wainwright, 27, left the field in the fourth minute at the Stade de France after taking a blow to his head but suffered no facial fracture or concussion.
“He doesn’t have that fracture, so we are pretty hopeful he will be available,” said forwards coach Jonathan Humphreys.
“He had an unbelievable gash. That’s the thing for us. He’s a tough kid and he’s like ‘I’ll be all right, they can just stitch me back up’, but it’s a pretty bad gash.
“He’s got eight days to turn around [between games] so we are hopeful, especially since he’s desperate to play.”
Faletau and Wainwright will have to prove their fitness in the final couple of training sessions before the game.
Scarlets back row Taine Plumtree has joined up with the squad, while James Botham switched from flanker to number eight during the game in Paris.
