B757 captain reported encountering a near miss with another taxiing aircraft.

Narrative:

During pushback; ramp directed we push back far enough so a heavy jet could enter the ramp and proceed to the gate. As we were pushing back; not yet in place; both my first officer (first officer); and I noticed the heavy jet begin taxiing. My first officer commented; what is he doing; and when I looked up it appeared the right wing of the heavy jet was going to hit our flight deck windows. Luckily this did not occur but it was too close for our comfort. What is the hurry - do we not all get paid by the minute. This is simply not acceptable. I called ramp to ask whether or not this was a revenue flight and was told this was aircraft Y arriving from ZZZ1.the inbound all night flight's captain decided to taxi before we were fully clear of their wing. Do not be in such a hurry to taxi and ensure you are fully clear of another aircraft before beginning your taxi. The company has had too many ground collision events over the last two years - and I guess the message has not gotten out to all the crews.

Original NASA ASRS Text

Title: B757 Captain reported encountering a near miss with another taxiing aircraft.

Narrative: During pushback; Ramp directed we push back far enough so a heavy jet could enter the ramp and proceed to the gate. As we were pushing back; not yet in place; both my FO (First Officer); and I noticed the heavy jet begin taxiing. My FO commented; what is he doing; and when I looked up it appeared the right wing of the heavy jet was going to hit our flight deck windows. Luckily this did not occur but it was too close for our comfort. What is the hurry - do we not all get paid by the minute. This is simply not acceptable. I called Ramp to ask whether or not this was a revenue flight and was told this was Aircraft Y arriving from ZZZ1.The inbound all night flight's Captain decided to taxi before we were fully clear of their wing. Do not be in such a hurry to taxi and ensure you are fully clear of another aircraft before beginning your taxi. The company has had too many ground collision events over the last two years - and I guess the message has not gotten out to all the crews.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1702001
Time
Date	201911
Local Time Of Day	0001-0600
Place
Locale Reference	ZZZ.Airport
State Reference	US
Aircraft 1
Make Model Name	B757-200
Operating Under FAR Part	Part 121
Flight Phase	Taxi
Flight Plan	IFR
Aircraft 2
Make Model Name	Commercial Fixed Wing
Operating Under FAR Part	Part 121
Flight Phase	Taxi
Flight Plan	IFR
Person 1
Function	Captain
Qualification	Flight Crew Air Transport Pilot (ATP) Flight Crew Instrument Flight Crew Multiengine
Events
Anomaly	Conflict Ground Conflict Critical Ground Event / Encounter Other / Unknown