Diddy's federal trial may begin without one of the biggest witnesses for the prosecution ... 'cause the feds still can't get in touch with the woman known as "Victim 3."

The third day of jury selection in Diddy's federal case wrapped up just a short time ago ... and, the prosecution told the judge they still haven't been able to locate this unidentified person or get through to their attorney.

As we told you ... the prosecution, led by Maurene Comey, admitted Monday that Victim 3 does not live near New York City -- and, try as they might, they're worried about getting her to show up in person.

Even if she's subpoenaed, prosecutors told the court, they're not sure she will show up.

Diddy's team asked the judge to tell prosecutors they needed to share their plan as it pertains to Victim 3 with the defense by the end of this week ... and, the judge pushed prosecutors to make every effort to contact this woman and her attorney.

There won't be anyone in court tomorrow ... but, both sides will be back at the courthouse Friday -- where they will start whittling down the jury pool from 45 to the 12 jurors and six alternates needed for trial to begin.

The prosecution has already shared the identity of the first three witnesses they plan to call on Monday and Tuesday ... two witnesses whose testimony will be fairly short on Monday -- and one who will take up some of Monday and all of Tuesday.

The trial's moving forward ... whether the prosecution has all their star witnesses or not!