The women, believed to be mother and daughter Karen and Jade Hales, were found at a property in Cathedral Road, Anfield, at about 09:50 BST following a report of concerns for their safety.
Officers described the deaths as unexplained. Post-mortem examinations will take place later.
The investigation is in its "very early" stages, Merseyside Police said.
Locals said the younger woman looked after her mother as her carer, and was seen regularly walking her dog, Tyson, a Staffordshire Bull terrier.
Samantha Parkin, 25, a friend of 28-year-old Jade, said she was in contact with her last night via the social media site Instagram.
Ms Parkin said: "She stopped messaging me last night about half seven.
"She was bubbly, she was funny, she was dozy, she was kind.
"She would do anything for anyone. She loved everyone who came into contact with her.
"It's the worst thing that has ever happened to me. I'm going to miss her."
Another local, Ellie Bleasdale added: "She was a lovely girl - wouldn't hurt a fly, a sound girl."
A 42-year-old man has been arrested on suspicion of murder after the bodies of two women were found in Liverpool.