The Ukraine captain confirmed his competitive career was over after a 1-0 loss to England on Tuesday, which eliminated his team from the European Championship.
However, Shevchenko wants to play one last match for his country to thank his fans for their support throughout his career.
"If it's possible, I will play one more game,'' Shevchenko said. "It will probably be one of the friendlies. I will ask for the organization of this match.''
It wasn't a fitting end to his 111-match international career in which he scored 48 goals - more than three times as many as any other Ukrainian player.
Shevchenko didn't start the must-win match for Ukraine because of a left knee injury and came on as a substitute in the 70th minute. Fans chanted "Sheva, Sheva'' but he couldn't help the team mount a comeback.
Long before Euro 2012, Shevchenko announced that the tournament would be his last after persistent knee and back problems weighed him down in recent seasons.
He is not the predatory striker he was in his heyday when he regularly scored more than 20 goals per season for AC Milan, and he recently said he would not be able to play three full matches a week.
Still, Shevchenko proved to be of great value for Ukraine at Euro 2012, scoring twice in helping the co-host beat Sweden 2-1 in their opening match last week.
The 2004 European Football of the Year, who is without a club after his contract at Dynamo Kiev expired, believes the Ukraine team has a fruitful future ahead without him.
"I think there is a time to give the opportunity to the younger players,'' Shevchenko said. "They have a very good future.''
The striker said the squad's younger players have gained valuable experience at Euro 2012 - only the second major football tournament in which Ukraine has taken part besides the 2006 World Cup in Germany.
"It will really give them the opportunity to feel stronger and feel they have played at the highest level of European football,'' Shevchenko said. "I will give them an opportunity to play.''