The subject of children was brought up in a speech by the father of the bride, Ramzi Alamuddin during the wedding ceremony, reported Hollywood Life.
Ramzi used his speech to say, "Now it's time for grandchildren."
This is the second marriage for Clooney, 53, who married Talia Balsam back in 1989 - and the first for 36-year-old Amal.
The pair were married in Venice, where the world's media descended to get a glimpse of the happy couple.
The wedding was a star-studied event, with Matt Damon, Bill Murray, Bono and Cindy Crawford amongst the A-list guests.
Clooney and Alamuddin exchanged vows that they had written themselves, before the guests tucked into a five course meal.
The couple made their marriage official at a civil ceremony in Venice.