The accident, which claimed the lives of four other passengers, left the pair badly burned.
Barker, 32, who not only played drums in the platinum-selling band but also starred in his own MTV reality show, and Goldstein, 35, known as DJ AM, were said to be in a critical but stable condition.
Those killed in the crash on Friday night included two members of Barker’s entourage, Chris Baker, 29 and Charles Still, 25.
Pilot Sarah Lemmon, 31 and co-pilot James Bland, 52, were also killed.
The jet was en route to Van Nuys in Los Angeles, California, when it veered off the runway and crashed through a fence before smashing into a mound of earth and bursting into flames.
It took off just hours after Barker and Goldstein’s show on Friday, which included performances by former Jane’s Addiction singer Perry Ferrell and singer Gavin DeGraw.
Investigators have recovered the black-box and are trying to discover what caused the accident.
The two passengers who died, Mr Still and Mr Baker, worked for rock star Barker. Mr Still, nicknamed Che, was a longtime friend of Barker and sometimes worked as a bodyguard when the drummer performed in small shows.
Mr Baker, nicknamed Lil’ Chris, worked as a personal assistant to the drummer and had appeared occasionally on MTV’s “Meet the Barkers”, the domestic-life reality show that followed the drummer, his wife and their children in 2005 and early 2006.