Pep Guardiola, who took over at the Etihad Stadium in the summer, has guided the team to nine straight victories in all competitions.
The Spaniard arrived in the North-West city with high expectations on his shoulders given that he has won 21 trophies across spells in charge of Barcelona and Bayern Munich.
Villa, who now plies his trade in the USA with New York City FC, won two La Liga titles and a Champions League trophy under Guardiola at Barcelona.
“Guardiola has done this at different clubs, which is amazing,” Villa told NBC. “When I was at Barcelona he was tremendous, going to Bayern he was excellent and now at Manchester City he’s gotten off to a great start as well.
“He’s very good and I’m very proud to have worked with one of the best coaches in the history of soccer and to see him putting up some great results.
“He’s brought great tactics to all the clubs he’s been at and the players really like playing for him. I think City’s start has shown how good of a manager he is. I think they’ll be one of the best clubs for as long as he’s there because he’s very smart and always looking to get better.”