A321 Captain reported while stopped during taxi another taxiing aircraft making a turn almost came in contact with the aircraft nose and flight deck windows. Captain stated the other aircraft corrected their path at the last moment and passed 20 feet from reporter's aircraft.

Narrative

All events leading up to initial taxi out from the gate at ZZZ were uneventful. After single engine start; FO requested taxi clearance with Ramp Controller via ACARS Silent Taxi. Our clearance was to taxi North on the '1' taxi line to the north ramp and to contact ZZZ for further clearance. Ramp Controller also instructed us to taxi as up to the Hold Line for traffic behind and to keep it tight ". As we got near Taxiway 1 North; my FO and I stopped monitoring Ramp Controller and make initial contact with ZZZ. As I was taxiing near the hold line ( note the boundary hold line is just north of the vehicle service road) I noticed a company aircraft traveling Eastbound on taxiway '2' making a right turn for the ramp and proceeded to park at Gate X. I stopped just short of the vehicle service road so as to allow room for that aircraft to approach and park at Gate X. This is where I stopped our aircraft. You will see from my attached pictures where we stopped.At this time I stopped our aircraft and we were now monitoring ZZZ Ground on frequency for further taxi clearance. Off to our Right was a 737; at the top of the 'Taxiway 3' North line. Ground Controllers first gave clearance to Aircraft Y to taxi to Runway XXR via a left turn onto taxiway '4'.My FO and I were immediately alarmed to see the crew in the 737 begin a tight left turn towards taxiway '4' via the yellow centerline right to the left of them. Please note from the Jeppesen 20-9 image that there is indeed a yellow taxi centerline from the Taxiway 3 North line to taxiway' 4'. It's also worth noting that that centerline was intended for aircraft entering the taxiway 3 North ramp taxiing Southbound as that was a normal taxi flow pre-construction here at ZZZ. Prior to construction beginning; it was normal for Ground Control to issue aircraft a clearance from the North Ramp to make a Left turn onto '5' and '6'.In this morning's situation; the Captain taxiing Aircraft Y appeared to NOT clear his left side as he began a left turn taxi towards our parked aircraft. The Captain of that aircraft was steering as to align his seat over the centerline. I was seconds away from ordering my FO to evacuate the Flight Deck towards the cabin as it was appearing that the 737 split semitar wingtip was tracking to make contact with our aircraft nose and Flight Deck windows. The Captain of that aircraft did notice us prior to passing abeam and made a corrective turn to the right to avoid contacting our aircraft. I believe the wingtip of that aircraft eventually passed us 20 feet from our aircraft nose. In my XX years at Company; I have NEVER seen an aircraft this close to making contact! If I had parked my aircraft at the hold line as the Ramp Controller intended; I'm sure that aircraft would have made contact with ours.It's worth noting that during construction; ALL aircraft at ZZZ now depart the alley via the north ramp. While I fault the crew of the 737 for not clearing their left wing before turning towards us; I also believe that yellow taxi line SHOULD be removed. A taxi centerline that doesn't provide proper clearance MUST be removed. At night or in reduced visibility; a crew would be lulled into following this taxiway centerline which will NOT provide clearance from an aircraft parked at the 'Gate 2' North line."