The world number 15 decided to quit the elite men's team competition earlier this year, saying he wanted to give the younger Russian players a chance to play for their country.
"If everything goes well, I'll be in Kazan," Youzhny said in reference to the September 16-18 tie in the city on the Volga River.
"We're in a tough situation right now and I thought it was my duty to help the team. Therefore, I've made myself available for that tie."
Russia, who have won two Davis Cup titles in the last decade, have had a lean spell in recent years following the retirement of former world number ones, Yevgeny Kafelnikov and Marat Safin. They could be knocked out of the World Group for the first time since 1992 if they lose to Brazil.
Youzhny, however, did not commit himself to the Davis Cup any further, saying he would asses the situation each time.
"I would still love to give younger players a chance but if our captain says he needed me next time it would be difficult to turn him down," the 29-year-old said.
Youzhny become a national hero after he clinched Russia's first Davis Cup title with a dramatic 3-2 victory over holders France in the Paris final in 2002.
A late replacement for Kafelnikov, he fought back to beat Paul-Henri Mathieu in the decisive fifth rubber, becoming the first player in the Davis Cup's 102-year history to win a match in the final after losing the first two sets.