Chapter 2 - Kinematics: Description of Motion - Learning Path Questions and Exercises - Conceptual Questions - Page 59: 5

Yes, it is possible for the jogger's instantaneous velocity to be negative.

Velocity is a vector quantity. Let's say the jogger's average velocity is along a positive directed axis. If part of the jog is done along the negative direction, the jogger has a negative instantaneous velocity at the time.