Air carrier pilot reported Ground Control issued taxi instructions to cross a runway. Approaching the hold line the reporter noticed an aircraft on short final and stopped taxiing.

Narrative

In ZZZ we had just pushed back from Gate X to spot X. We started the right engine during push back and disconnected from the tug; everything was all normal. We ran the after start and taxi checklist as normal; we were planning to takeoff Runway XX. The First Officer called ground for taxi and ground gave us the instruction to taxi to Runway XX via kilo; cross runway XY." After receiving these instructions I started the taxi and called for delayed engine start. I started moving the aircraft slowly to Runway XY at kilo to cross as instructed. At about 30 ft. from the hold short line of Runway XY at kilo I noticed something out of the corner of my eye that looked like an aircraft and stopped our aircraft immediately. Right after that a Aircraft Y landed on Runway XY. After the Aircraft Y landed ground announced "Aircraft X stop; hold short of Runway XY." At this point I was already stopped with the taxi light off knowing I was not moving until they figured out what was going on. After that another Aircraft Y landed and taxied off the runway. At that point we were cleared to cross Runway XY. The rest of the flight continued without further incident.Suggestion: Better communication either between tower and ground so ground would know there is an aircraft on approach for runway XX. To better communication with ground and the taxiing aircraft."