The country's football association says that Anatoliy Tymoshchuk should be stripped of his titles because of his role at Zenit St Petersburg.
An assistant coach at the Russian club has been 42 years old.
He has yet to speak out against Russia.
The Ukrainian Association of Football says that his choice to continue at Zenit damages the image of Ukrainian football.
Between 2000 and 2016 Tymoshchuk made over 100 international appearances.
Tymoschuk AA, the former captain of the Ukrainian national team, did not make any public statements regarding the beginning of Russia's military aggression against Ukraine, according to a statement from the UAF's ethics and fair play committee.
Tymoshchuk won league titles with Shakhtar and Zenit and was a part of the team that won the treble. He was the captain of his country.
At a time when another former club, Bayern Munich, publishes statements and holds actions in support of Ukraine, Tymoshchuk continues to remain silent and work for the club of the aggressor.
In addition to calling for Tymoshchuk to be stripped of his coaching licence, the UAF wants to exclude him from the official register of national team players.
Several Ukrainian sports people, including tennis player Sergiy Stakhovsky and boxer Oleksandr Usyk, have joined the military effort in response to the Russian invasion.
The brothers Vitali and Wladimir are defending their homeland, as well as Olympic karate medallist Stanislav Horuna, who spoke to Radio 5 Live about joining his country's defence against Russia.
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