Can Curve25519 be used for pairing-based cryptography?

We usually need pairing-friendly curves in order to use them for bilinear pairing computation. Is Curve25519 a pairing-friendly curve? If not, can we still use it for pairings and how much more inefficient would a pairing computation on this curve be compared to a BN curve?

For Curve25519 the degree is 1206167596222043702328864427173832373476186059896651267666991823047575708498 $\approx 10^{75}$, mapping to a $\approx 3 \cdot10^{75}$ bit field. It's rather unlikely that you could afford a computer which can store an element of this field or perform computations on it.