Does an object rotating in place have linear momentum?

I understand that an object with linear momentum could have angular momentum. However, can the same be in reverse? For example, will a wheel spinning in place be considered to have both angular and linear momenta? It will have tangential velocity, but the wheel itself is not moving in a straight line. Could you use its tangential velocity and say it has linear momentum?

• Linear momentum of a massive body is given by $m v_{cm}$. So a wheel rotating in place should not have linear momentum as a whole as it's center of mass is not moving. – harshit54 May 4 at 14:27

$$p_\text{ non-centre-particle}\neq 0$$
$$\sum p_\text{ particle}=p_\text{ total}=0 \qquad \text{ if centre-of-rotation is CoM}$$