Clooney, 53, married Alamuddin, 36 last month in Venice, Italy, reported the Daily Star.
"Before meeting Amal, George had come to terms with the fact he wasn't going to have children and despite always wanting to be a dad, he had convinced himself it wasn't going to happen.
"Meeting Amal changed everything and he told pals how he couldn't wait to make 'mini Clooneys' and hoped they took after their mother and inherit her Lebanese beauty with her dark and striking characteristics," a source said.
"They vowed to start trying as soon as they tied the knot and have told friends they can't wait to be parents and want to have at least three children," the source said.
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While Alamuddin apparently wants to keep working post motherhood, Clooney is said to have promised to make children his only priority.
"She has already made it very clear that she won't sacrifice her career ambitions and will hire a team of nannies and child-minders.