I cooperate with one of the persons involved in that conflict.
If you mean that he is a "work friend" you advise him/her later that it looks as bad on them as it does on the other person.
Their manager is not around (he sits in other open space). Should I report to their manager?
Going to someone else's manager about something is generally a bad idea (unless it is an emergency - if one person is threatening the other it is an emergency).
Should we try to solve the problem without mangers?
We? If you weren't involved, then you should stay out of it (see exceptions below).
Make a note to yourself about when it started, who is shouting and what the conflict appears to be about - then you can go for a walk around the block, go to the bathroom, or something else to remove yourself from the situation.
If it frightens you - you can talk to your manager about that part of it. And I mean if you are actually afraid of something, not just really uncomfortable (as most people would be).
If it continues to happen - you can talk to your manager about it.
This answer assumes two people of relatively equal power - if one is bullying the other then you can skip the rules and help your friend.