Forward Salah, the Reds’ top scorer with 23 goals in all competitions this season, has missed the last two matches because of a groin problem.
Sturridge has not been involved in a game since the Champions League victory over Spartak Moscow on December 6 having suffered with illness and injury.
Liverpool announced on their website on Wednesday that the pair had taken part in a session earlier in the day at Melwood.
Sunday’s encounter with City at Anfield will be fourth-placed Liverpool’s first match since the departure of Brazil playmaker Philippe Coutinho to Barcelona.
Coutinho signed a five-and-a-half-year contract with Barca on Monday as a transfer that could be worth up to £142 million to Liverpool was finalised.
Liverpool forward Roberto Firmino, his compatriot, on Wednesday posted a message on Instagram saying “Liverpool is no longer the same without” the “magical” Coutinho.