Eva, 40, has reportedly been put on bed rest following strict orders from her doctor.
It's not known why the star has been instructed to take this measure, but it's not uncommon for women in the later stages of pregnancy to be advised to rest as a precautionary measure.
A 'source' close to the star told People magazine that in the last few months, Eva has 'barely left the house.'
"Ryan has been taking care of her," the source added. "Picking up food and running errands. He has been very supportive about keeping things a secret."
Although Eva and Ryan, 33, have kept quiet about their impending parenthood, people close to the pair have been less tight lipped.
According to another 'source', Eva has been using methods touted by old wives' tales to predict whether she'll have a boy or a girl.
"Her bump sticks out more in the front than sideways and she thinks that means she's carrying a boy," an insider told the American edition of OK! magazine.
If Eva is right, it's been suggested that the pair may choose to name their baby Thomas - which is Ryan's middle name. However, if they have a girl, the names currently said to be top of their list are Donna - Ryan's mum's name, or Coral after Eva's mother.