A close pal told Life & Style magazine: "Jacqui's having a boy!"
The couple are currently in Beverly Hills and eyewitnesses reported they looked blissfully happy together.
A source said: "They seemed very happy together. Jacqui kept rubbing her belly and tousling Guy's hair. They were just having a leisurely morning and enjoying private conversations with each other."
Ritchie and Ainsley have reportedly been hoping to start a family for some time and he is determined she should have a stress-free pregnancy.
A friend said: "They have been keen to start a family for a while now. They're absolutely made up. We expect to hear wedding bells next year.
"Jacqui was crying with joy when she found out she was pregnant. They went on holiday because Guy is determined she takes it easy. He won't let her do anything more strenuous than argue over baby names."
Ritchie split from Madonna in 2008 after almost eight years of marriage.
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