When a mass moves towards a bigger mass at a constant velocity, they will be attracted to each other such that the smaller mass will revolve around the bigger mass with the same speed as before.
However, if the above case is true, the total angular momentum of the system will increase from zero to non-zero. This is clearly a violation of conservation of angular momentum.
Edit: when I am talking about this, I don't mean that two mass are moving towards each other. I mean for instance there is a stationary planet and a mass such as an asteroid move horizontally above the planet at a constant speed. The asteroid is moving past the planet without touching it. This asteroid will then be attracted to the planet gravitational pull, resulting in it turning direction and begin to revolve around the planet. This is just hypothetical and I don't see how this is impossible.