Is it possible to reverse Diffie-Hellman key exchange?
It is certainly possible given enough compute resources.

However, if you mean to ask whether it is computationally feasible for an eavesdropper to derive the private keys, then- no, it is not.

Refer to the secrecy chart on Wikipedia: 

The private keys a and b are meant to be known only to Alice and Bob respectively.

In the real world, the Logjam attack is one example of how adversaries with nation state-level compute resources (such as the NSA) could theoretically break Diffie Hellman implementations, relying on the fact that a small set of primes were used across most common implementations.