When the sun is used as the frame of reference, the Earth is constantly moving around the Sun. And so is a body that lies on the Earth. Even a body which may appear to be stationary on the Earth is moving around the Sun.
The movement results in a kinetic energy that is given by the relation KE = (1/2)*m*v^2, where m is the mass of the body and v is the velocity of the body in the reference frame of the Sun.
To have a zero kinetic energy in the frame of reference of the Sun, we would have to be still and have the same location with respect to the Sun. This is not possible to do, as attempting the same would result in our collapsing into the Sun due to the gravitational force of attraction.