While a source described Odom as "happy and ecstatic" about the pregnancy, the insider added the NBA star was concerned about his child appearing on television.
"They're really happy, but Lamar is a little weary of exposing his baby on TV," the source told RadarOnline. "He already doesn't like his life being played out for everyone to see eight months of the year."
Kardashian allegedly wants to keep the pregnancy announcement mum until it can be announced on Keeping Up With the Kardashians, according to RadarOnline, which added she'd also like to wait until she passes through the first trimester.
Kardashian was reportedly "inspired" to become a mother after her sister Kourtney Kardashian welcomed son Mason Dash Disick in December.
Odom already has two children from a previous relationship.