The Gravity star is said to have popped the question and Alamuddin was spotted wearing a large ring to dinner with Clooney, Cindy Crawford and Edward Norton at a restaurant in California, according to E!.
Alamuddin, 36, was born in Beirut and specialises in human rights and international law, having represented Wikileaks founder Julian Assange and former Ukrainian prime minister Yulia Tymoshenko.
She and Clooney, 52, have been seen spending time together in New York, Tanzania and the Seychelles.
The Descendants star Clooney was previously married to actress Talia Balsam and has said that he would never marry again.
Clooney has dated a string of beautiful women including Lisa Snowdon, Stacy Keibler and Elisabetta Canalis, but as recently as 2012 his sister Adelia Zeidler said: "George will probably not get married. He decided that he could have the career or he could have a family."