The 34-year-old actress is expecting her first child with her partner of 15-months Brian Hallisay and she wants to pay tribute to her late mother, who died in June 2012 aged 67 from cancer, reported National Enquirer magazine.
If they have a girl, the tot will share her grandmother's moniker, and if they have a boy they will call their son Patrick.
"The loss is the only thing casting a shadow over her baby joy," the source said.
Jennifer is believed to have promised her mother she would find a good man to settle down with and raise a family to her mum before she passed away.