Gyan, Ghana's all-time top scorer, hit a landmark 50 goals in 103 appearances as the Black Stars thrashed Ethiopia 5-0 in the Africa Cup of Nations qualifiers last week.
“Gyan has been a wonderful leader. He is great and has done a lot for the national team,” Badu said on GHOne TV.
“For now, he is the all-time top scorer and just recently he was able to score his 50th goal, which is a very wonderful achievement.
“I just hope he wins the Nations Cup title with the Black Stars to crown his achievement.
"I will be happy if he leads the team to win the trophy.”
Gyan, 31, is one of just two Ghanaian players to have played at three Fifa World Cup tournaments.
Not only is he the historic scorer of Ghana's first ever goal at the competition, he is also Africa's highest scorer at the global showpiece with six goals.
At the Africa Cup, the striker holds Ghana's record of the most tournament appearances, having played in six editions between 2008 and 2017.
The Al Ahli frontman is, again, Ghana's joint-all-time scorer at the Afcon with eight goals.