In an apparent sign that Senator Elizabeth Warren will not be named Hillary Clinton’s running mate, Ms. Warren was invited by Mrs. Clinton’s campaign on Tuesday to deliver a prime-time address on the first night of the Democratic convention this month — a marquee speaking slot but one that is earlier than vice-presidential picks typically appear.

Such nominees usually speak later in the convention week to build anticipation for the top of the ticket.

Two Democrats briefed on the invitation to Mrs. Warren, however, cautioned that Mrs. Clinton had not yet made a decision about a running mate and that asking Ms. Warren to take the stage on the first night did not preclude her from being tapped as the vice-presidential nominee.

Ms. Warren and other individuals who received invitations on Tuesday to address the Philadelphia convention were told that their speaking times were subject to change depending on who was selected for vice president, according to the two Democrats, one with ties to Mrs. Clinton and the other to Ms. Warren, who both spoke on the condition of anonymity because they were not authorized to publicly discuss convention planning.