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The singer announced that she was expecting her first child with husband Marc Anthony in November and is rumoured to be due to give birth in the spring.
According to Star magazine, her mother Guadalupe was spotted picking up baby ID bracelets engraved with the names Max and Emme at a New York jewellery store.
Newsday also reports that Lopez has been admitted to a Long Island medical centre under a pseudonym, although a hospital spokeswoman denied the claims.
The newspaper quoted a source at the facility as saying that the 38-year-old was "in the house".
Lopez recently revealed that she is to take an extended break from work to focus on caring for her baby.
