Recognition of forward edge requires say for a Edge A->B, B should have been visited before the edge A-B is discovered and this can happen only when B is visited via some other vertex using more than one edge.Since, BFS finds shortest path from source in terms of smaller number of edges, When Vertex A is enqueued, edge A-B will be discovered and marked a tree or cross edge.Hence forward edges never possible.

What is forward edge? Let there is a tree edge between A to B and B to C then A --> C is a forward edge, think that At A itself C is pushed into queue then there is no chance of A --> C is look as forward edge