A pilot can file a Near Midair Collision Report if in his judgement the aircraft were too close. There is no standard required to file the report.

That being said, it is likely that part of your flight was conducted outside of class A or B airspace where there is no minimum separation standard. In the United States, only flights operating under instrument flight rules receive ATC separation outside of class A or B airspace. Pilots are required to see and avoid each other during visual conditions.