The Keeping up with The Kardashians star and her rapper husband are already parents to daughter North, who turns two on Monday.
Kardashian's tweets follow a US Weekly report, citing multiple unnamed sources, that she is expecting a boy.
Read more:
• Kim Kardashian blames angry Twitter outburst on pregnancy
• Kim Kardashian pregnant with second child
"Kanye loves Nori more than anything, but to make his world complete he wanted a little boy, an heir," a source close to West told the website.
"He's overjoyed!"
An unnamed friend of Kardashian is quoted as saying: "Kim always wanted two kids.
"A girl and a boy."
- AAP