Speaking to Olympics.com's Indira Shestakova in a recent Russian-language interview, he said: "We even talked to Zhenya [Medvedeva] personally.
"I told her, 'Why wouldn't you try pairs, make some noise?' But usually, the answer was no."
Since then, a combination of the Covid-19 pandemic and injuries have kept her out of ISU events – but she has begun skating ice shows with a male partner.
"Not pair skating"
Medvedeva, who won silver at the 2019 Rostelecom Cup before withdrawing from that year's Russian national championships after the short program, saw her 2020/21 season affected by a chronic back injury.
She also contracted Covid-19, which she later recovered from.
While Trankov believes Medvedeva's ability as a skater means she will have no problem performing in shows with a partner, he does not see a route to her switching disciplines competitively.
"What Zhenya is doing right now is not pair skating. It is called adagio [skating] when a boy just lifts you up and you do some beautiful spectacular elements," he explained.
"That's not pair skating, not sport pair skating: there are no multi-turn throw jumps, twist lifts; there is no big risk. That's more for the art of ice shows.
"I think Zhenya is doing the right thing in principle, because if she is a well-rounded figure skater she will be able to perform in the ice shows not just as a single skater, but also with a partner," Trankov adds.
"That flexibility is always very welcome. [But] I don't think that Zhenya Medvedeva will change her sports role. It's going to be very difficult to do."
Would it be plausible for someone like Medvedeva, a successful ladies' singles skater, to attempt the switch?
"It's realistic, but it depends at what level you want to perform," Trankov explains.
"You need to find a partner, you have a lot to learn, plus the injuries she has had… it also has an impact."
Co-coaching with Tutberidze
Trankov is the pairs coach for two-time European champions Evgenia Tarasova and Vladimir Morozov, but recently the three of them – alongside Pavel Slusarenko, coach of 2020 World Junior champions Apollinariia Panfilova and Dmitry Rylov – spent time working in Novogorsk alongside Eteri Tutberidze and her team.
Tutberidze is perhaps more well-known for developing Russia's constant train of ladies' singles skaters, having had a hand in bringing through Medvedeva, Olympic champion Alina Zagitova, world champion Anna Shcherbakova, world junior champion Kamila Valieva, Alexandra Trusova, and Alena Kostornaia among others.
"The pairs skating details [rest on] the pairs coaches, in this case me and Pavel," Trankov says.
"The rest is on Team Tutberidze. Sergei Dudakov, Daniil Gleichengauz, everyone helps. They also listen to my and Pavel's opinions in terms of choreography.
"No one hogs the blanket for themselves, we work together. Eteri is a very cool motivator, and what the guys have been doing in June is something they've never done before.
"For all of us, including me, it breaks the mould. I was sure before that something is impossible, but Eteri Georgievna [Tutberidze] proves at every training session that nothing is impossible. There is, of course, a big difference in that regard. That's probably why they have results like that."
Learning as a coach
Trankov, who has worked alongside Marina Zueva while training Tarasova and Morozov, says he is growing as a coach seeing how Tutberidze works.
"I take good notes of everything when dealing with all my coaches, I learn from all the coaches I've worked with myself as an athlete," he says.
"I learned a lot from Marina Olegovna Zueva. She's on the top for me right now, number one, because I worked with her for a year and in that year I learned so many things that I hadn't in my entire career.
"Right now, of course, I totally can learn from Eteri Tutberidze. Above all she is an obsessive super professional, obsessed with the result, obsessed with her athletes.
"And she is so deep in what she does... I was in shock."