"The family is extremely private, just like Bowie," the source adds. "Bowie had a tiny, tiny circle of friends and confidantes."
The rock icon died Sunday after an 18-month battle with cancer. He is survived by his wife of 24 years, Iman, their 15-year-old daughter Lexi, and his son Duncan Jones, 44, from his first marriage to Angela Bowie.
Shortly after Bowie's death, Duncan returned from New York to L.A., a source close to the family tells PEOPLE.
"Very sorry and sad to say it's true. I'll be offline for a while. Love to all," Duncan Tweeted early Monday morning.
Very sorry and sad to say it's true. I'll be offline for a while. Love to all. pic.twitter.com/Kh2fq3tf9m-- Duncan Jones (@ManMadeMoon) January 11, 2016
The singer had turned 69 just two days before his death; on the same day, his latest album, Blackstar, was released.
Just hours before news of his passing made headlines, a tribute concert honoring the star was announced. Now, The Roots, Cyndi Lauper and more will memorialize him at a Carnegie Hall show in New York on March 31.
Since his death, Bowie's fans, friends and peers began commemorating the singer, posting tributes online and creating shrines around the world.
"His death was no different from his life – a work of Art. He made Blackstar for us, his parting gift," Bowie's producer Tony Visconti wrote on Facebook Monday. "I knew for a year this was the way it would be. I wasn't, however, prepared for it. He was an extraordinary man, full of love and life. He will always be with us. For now, it is appropriate to cry."