Jason LaBar -- Kohberger's extradition hearing attorney -- tells TMZ his client is, for now, likely to waive his right to have his looming transportation back to ID heard in front of a judge ... which, if it holds true, would mean Kohberger will get shipped back Latah County this upcoming week without any further delay -- where he'd be expected to enter a plea.

While LaBar notes Kohberger has neither denied or admitted to the charges against him -- implicitly or explicitly -- he did say his client told him he felt he would be exonerated, which obviously suggests he believes he's innocent.

We're told Kohberger and his parents are shocked by his arrest -- telling us their home in PA was descended upon by feds very early Friday morning ... where they were surrounded by law enforcement and instructed to comply, which LaBar says Kohberger did without issue.

Part of the reason Kohberger might wanna get this over with quickly has to do with the fact he told his attorney he wasn't on the run. On the contrary, LaBar says Kohberger relayed that he and his father drove a white Hyundai from Washington -- where Bryan currently attends university -- back to PA on Dec. 18 ... a plan they'd apparently had all along.

The implication ... Kohberger was neither in hiding nor fleeing, as the murders occurred in mid-November. Remember, though ... Kohberger was within a stone's throw from the University of Idaho during this time -- pursuing a graduate's degree in criminology at Washington State University -- so this supposedly chill father-son road trip doesn't really clear him one way or another. It simply explains his movements during the holidays.

Of course, Kohberger has time to change his mind on the extradition hearing -- which could jam things up. Otherwise, court proceedings will begin and prosecutors will have to show their cards on what exactly they have that implicates him as the quadruple murderer.

There have been reports saying Kohberger has been getting surveilled for a while now, and that the feds were tracking his whereabouts these past few weeks. Also, the word is that the police have DNA evidence -- putting him at the scene of the crime -- and a match on the Hyundai seen in the area that night ... which they've reportedly traced to Kohberger.