Air carrier Captain reported a near miss while parked at the gate with an aircraft that was under tow. The conflict was observed by ramp personnel who informed the Captain in the cockpit of the conflict.

Narrative

While parked at Gate XX in ZZZ waiting to board for our flow time to ZZZ1; my First Officer (FO) noticed a ramper getting very animated on the ramp. A 777-300 was at the time being towed into the adjacent gate XY/XZ. The Ramper came up to the flight deck to report that he thought that the 777 wingtip came very close to our vertical stabilizer while it was being towed. He said wide body aircraft for several airlines operate out of that gate but none that big. While on the flight deck Ramper texted and then called his lead about the incident. He also took a picture of the 777 parked at the gate and of our aircraft parked at [Gate] XX and showed it to us. He then proceeded back to the ramp to continue his duties.A few minutes later; Ramper and the ramp Lead; came up to the flight deck. Lead said that he listened to what the ramper said and then looked at the path the 777 would have taken and came to the conclusion that the 777 wingtip did go over our aircraft's tail while we were parked and it was being towed to the next gate. Ramper did say that they had a wing walker on that side while it was being towed but the wing walker did not react or notice how close the wingtip got to our tail. They both reiterated that the wingtip did not touch our aircraft. The FO was on the flight deck at the time and did not feel any aircraft movement while this was occurring and he also went and looked at the tail after talking to the rampers. Ramper said he would file a report and asked me to file a report. He told us that various airlines normally park an Airbus A330 at that gate or a smaller 777 but not a 777-300. He said they would try to get video footage from the ramp regarding this incident. There are two lead in lines to that gate as it is labeled on the ZZZ [airport] 10-9 page as XY/XZ/XA. I am hoping this report will highlight this problem and prevent another such occurrence in ZZZ.