Moeaki suffered a fractured shoulder during his side's pre-season victory over the Pittsburgh Steelers on Saturday, although the full extent of the injury is as yet unknown.
Moeaki could potentially not miss any games if the injury turns out to be a minor one, but at the other end of the scale could miss a large chunk of the season should the problem require surgery.
Fasano is hoping that the former of those is true so that he can rekindle a growing understanding with the 26-year-old.
"I'm not sure exactly what injury Tony has right now, but if we were to lose him for any amount of time, it'd be a loss," Fasano told The AP.
"We did a good job in camp defining our roles as the tight end position is concerned in our offence, and we were really going to complement each other well, but hopefully it's not as major as people are making it out to be."
Fasano will embark on his first season with the Chiefs having joined in March this year.