updated 04/27/2014 AT 9:55 AM ET
•originally published 04/26/2014 AT 6:40 PM ET
His bachelor days are over!
A source with knowledge of the situation confirms Clooney popped the question and exclusively tells PEOPLE, “George and Amal are trying to keep things very low-key but they also aren’t really trying to hide this, it doesn’t seem. I think it’s like they want the people they love to know that this is real, that they plan on being together forever.”
The engagement happened “not that long ago, I think,” the source adds, and the couple don’t appear to have wedding plans in the works – yet.
On Thursday, the pair were spotted at Malibu hot spot Nobu with Cindy Crawford and husband Rande Gerber, who are longtime pals of Clooney’s. At the dinner, Alamuddin had a conspicuous ring on her left ring finger, a different source tells PEOPLE.
In addition, two sources say that witnesses at another L.A. restaurant, Craig’s, reported seeing the pair apparently celebrating their engagement with friends on Wednesday night, with Alamuddin sporting a “huge ring,” according to one.
A rep for the actor has only said, “I don’t comment on my client’s personal life.”