The attacking midfielder would be the third Nigeria Under-17 international to sign on at the Etihad Stadium following the African nation's success at the World Cup.
Yahaya scored four times in seven matches at the U-17 World Cup held in the United Arab Emirates, with Nigeria beating Mexico 3-0 in the final to win the tournament.
Dubbed the 'Nigerian Neymar', Yahaya had been tracked by Tottenham, as well as teams in Portugal and Spain, but City appears to have won the race for the 16-year-old and are in deep discussions with the player's agent, Babawo Mohammed.
The attacking midfielder, who plays at the Mutunchi Academy in his homeland, would become the third member of the African nation's junior team to join City and is keen to link up with his international teammates at the Etihad Stadium.
Yahaya, who describes Andres Iniesta as his footballing hero and has admitted he wants to play for Real Madrid, has remained coy over his immediate future in recent months.
"I am not going to talk on that one [where he wants to move], I have a manager in Babawo Mohammed. I have left that for him to handle. He knows me and knows what is good for me," he told MTNFootball in November.
Chidi Nwakali, meanwhile, is also on the verge of signing for the club after arriving for talks last week, with City opening its state-of-the-art Etihad Campus training facility in August.