Zagitova, who led after Wednesday's short skate, and Medvedeva both have their sights on gold - which could be the first for Olympic Athletes from Russia (OAR) at the Pyeongchang Winter Games.
"During the 2014 Olympics, I was only 14 years old and I remember the moment when our Russian team became gold medalists. It was really amazing. I was like – Yeah, I want the same feeling. I want to feel it," Medvedeva said at a news conference.
Medvedeva had set a new world record just moments before her 15-year-old rival and training partner Zagitova broke it, earning a record 82.92 points for her routine to "Black Swan".
"We're humans and we are friends, we're young girls. We can talk about everything to each other. When we take the ice, it's a sport, this is a real sport, and we must fight," Medvedeva said.
"Every competition is like a little war."
In her turn, Zagitova said the most important thing now is to give it 100 percent and have another clean performance on Friday.
"Evgenia and I are very good off the ice but during the time on the ice and during competitions I personally get this feeling of rivalry. It’s not bitter or personal, but it’s there," Zagitova said at the news conference.
Nothing seemed to disrupt Medvedeva's smooth path to Olympic glory until she suffered a broken foot and was beaten by Zagitova at the European Championships in January, her first loss in two-and-half years.
The team mates share renowned coaches Eteri Tutberidze and Sergei Dudakov, and also have a choreographer in common, Daniil Gleichengauz.
Should Zagitova win gold in the final on Friday, she will be the second youngest ever to do so. America's Tara Lipinski was also 15 when she topped the podium in Nagano in 1998, but was about a month younger than Zagitova is now.
Medvedeva said she has so many talented, young rivals in her country armed with difficult elements and jumps, and that "it just forces you to be stronger."
"Even though I try to focus on myself, there are still some lessons that show you have to be stronger. It’s a push forward," she said. "I try to do absolutely everything I can in the free skate."
(Reporting by Soyoung Kim and Elaine Lies in GANGNEUNG, Additional reporting by Gabrielle Tétrault-Farber; editing by Amlan Chakraborty)
