Faletau had hoped to return before the autumn internationals following a six-month injury lay-off with a broken shoulder, targeting his Cardiff return before the end of October.
The British and Irish Lions back row suffered this latest injury blow on his Cardiff comeback against Ulster in April.
Faletau’s injury was picked up in his first game for six months after he suffered a broken arm in Wales’ World Cup victory against Georgia in October 2023, while he also missed the 2024 Six Nations with a calf injury.
Adams last played for Cardiff in May against South African side Sharks before missing the final game of the domestic season, and he was also absent for Wales’ Tests against South Africa and Australia.
The British and Irish Lions wing featured for Wales in the 2024 Six Nations, where he battled through when he was not fully fit.
“We’ve tried to rest Josh over the summer in particular and get him back fit,” said Sherratt.
“He deserves to come back and be 100% fit, not 99%.
“Josh knows his own body. He’s not had a pre-season for five or six years. So we’ll give him all the time he needs.”
Cardiff captain Liam Belcher will miss the next couple of months because of a broken thumb, while fellow hooker Evan Lloyd is a doubt for the URC derby against Scarlets after picking up an injury in the 52-36 defeat against Glasgow last Friday.
Keiron Assiratti will be available this weekend but fellow Wales prop Corey Domachowski is a fitness doubt.
Sherratt also hopes to have flankers Thomas Young and James Botham and new centre signing Rory Jennings back in contention to play against Scarlets.