Sundsvalls Tidning cited unnamed sources “close to the couple” saying the baby was born on Wednesday, but did not elaborate on the claims, which remained unconfirmed by the couple.
But that did not stop Sweden from switching into baby joy mode, with some of the country's biggest newspaper quickly sharing the news.
Grant and Eberstein, a Swedish TV producer who is the daughter of Sundsvall-based politician Susanne Eberstein, already have one son together.
The pair have never confirmed their relationship status, but The Local could reveal official paperwork in October showing that they had bought a home together in the Swedish town of Torekov.
However it was later reported that Grant had handed in an application to the local authority in Båstad municipality to have the 122-square-metre property completely demolished.
Torekov is a seaside resort close to Båstad, one of the glitziest spots in Sweden, which hosts the Swedish Open tennis tournament each year. But although the town is already home to a number of celebrities, local residents seemed less than impressed about news of the purchase at the time.
“He has been here many times before, over several years. So it's not a big deal that he has bought a house here now,” Anette Bohlin, 58, told The Local, revealing that Grant “bought cinnamon buns at the local cafe here every day last summer”.
Hugh Grant already has two other children from his relationship with Tinglan Hong. His daughter Tabitha was born in 2011, while Felix was born a year later.