On the fourth spacewalk of this series planned for later this month, Koch and Meir will perform the world's first all-female spacewalk.
NASA paid tribute to Leonov on Friday.
His 12-minute spacewalk preceded the first United States spacewalk, by Ed White, by less than three months.
"We had this tradition that he would give cosmonauts pep talks before they board the spacecraft", Kononenko said. He was a friend of Yuri Gagarin, who became the first man in space in 1961 and trained with him.More news: Nikon's Z50 is official: the company's most affordable mirrorless camera yet
NASA interrupted live TV coverage of its second spacewalk this week to announce Leonov's death at age 85.
The first time a human stepped outside of a spacecraft was March 18, 1965, when cosmonaut Alexei Leonov took a leap of faith and science.
The two astronauts continued to replace nickel-hydrogen batteries with newer, more powerful lithium-ion batteries on the far end of the station's port truss.
Stanley Kubrick's 1968 film 2001: A Space Odyssey included recordings of Leonov's breathing in space.More news: 1,500 jobs lost, but unemployment rate declines in September
Leonov was also supposed to be the first man to land on the moon.
"His venture into the vacuum of space began the history of extra-vehicular activity that makes today's Space Station maintenance possible", Nasa said on Twitter. The special adapter allowing the spacecraft to dock was never used again, and it was not until USA space shuttles began visiting the Russian Mir space station that such linkups in space became routine.
Leonov helped train other cosmonauts before retiring in 1992, a year after the Soviet Union collapsed.
"It's a huge tragedy for us all", said the wife of cosmonaut Boris Volynov, Ms Tamara Volynova, who wrote a book about cosmonauts.More news: Tennis star Osaka to play for Japan
Leonov's funeral will be held next Tuesday at the Federal Military Memorial Cemetery in the Russian capital.