In an interview with Russian network RT, the Armenian trainer said: "I want to do something really good to turn Chen into an elite skater."
Chen, who in addition to his world titles has also won Olympic team event bronze, the Four Continents Championship, and the Grand Prix Final three times, would be considered 'elite' by many.
But according to his coach, Chen himself does not think he is an 'elite skater' yet.
"Not so long ago I talked about this with Nathan and honestly said that I don’t like a lot of things in his skating," Arutunian said. "Nathan answered, 'me too'.
"Many details can be improved and developed in all aspects," he added.
New programs and elements
Arutunian says the pair will continue to work on Chen's progress in the coming months, despite the current uncertainty during the coronavirus outbreak.
"Go to some dance schools, try new programs, come up with some new element, try to increase the total score," he explained of the duo's forthcoming plans.
"In the near future there are plans to open a skating rink for those who are professionally involved in sports, and allow three or four people on ice."
For now, Chen is jumping off-ice.
"We train in the park or on the beach, which is not prohibited. We do two workouts a day: in the morning, stretching; then physical training, strength and special training. Nathan jumps; I watch this from a distance and make adjustments," Arutunian said.
Russian skaters: "I don't want to get involved"
With Russian skater Alexandra Trusova announcing she would no longer be training under Eteri Tutberidze, some rumours suggested she would look to team up with Arutunian before Trusova confirmed she is now being coached by Evgeni Plushenko.
"Such stories almost always concern me," he said.
"Athletes turn to me often enough, including the Russian athletes. But I try to turn down some offers right away, because I don’t want to get involved.
"When I start working with a skater, I am interested in everything: how and where the child grew up, what he or she aspires to, how he or she is used to training.
"In the case of foreign skaters, I understand them quite well in this regard, but I don’t imagine very well how to work with a Russian athlete or with his or her parents. Because they grew up in other conditions, where they were provided with ice for free, where there was a group of coaches who controlled them from morning to evening, as I myself did when I lived in Russia.
"With Nathan Chen, for instance, I work on an equal footing. We are more 'partners'."
Break is "cool"
The long-serving coach says there have been some upsides to the break in on-ice work with his skaters.
"The general uncertainty is a bit confusing," he admitted, but added: "it was only at the start of everything happening when I suddenly realised to what extent I was tired from 45 years of work.
"While Nathan was taking exams at university, I was lying at home and thought to myself: 'how great it is not to be doing anything'. I never even suspected that it was so cool."