D4vd‘s parents aren’t surprised he’s behind bars — on suspicion of murdering Celeste Rivas — but, they don’t plan on giving up on their son …. TMZ has learned.

Kent Schaffer — the Texas-based attorney representing Dawud Burke and Colleen Burke — tells us D4vd’s folks are, obviously, upset and sad for their son, but they were well aware this was a strong possibility. As we’ve reported, LAPD’s viewed the singer as their suspect in the case for several months.

Schaffer says the Burkes didn’t speak to D4vd after his arrest Thursday evening, but he’s uncertain if they had a chance to do so on Friday.

As you know … a heavily armed police unit took D4vd into custody at the Hollywood Hills home where he was staying. He was booked into jail just after 10 PM Thursday, and he’s being held without bail.

D4vd’s was taken into custody more than 7 months after Rivas’ mutilated body was found in the trunk of his D4vd’s Tesla. While D4vd roamed free, a grand jury began to hear testimony back in November in connection with the case.

In February, the grand jury called Dawud and Colleen to testify … but, they’ve been fighting it — and Schaffer tells us they still plan on fighting it.

The lawyer says, “If the D.A. needs parents to testify, then they have no case. In my opinion, they’re just doing that for harassment purposes. If a proper subpoena was issued, they would’ve already spoken.”

D4vd obviously trusts his parents … remember, back in September, he transferred two of his Texas homes to his mother’s name.