The two Manchester clubs, who meet at the Etihad Stadium next Monday, are currently battling each other for the title.
With that in mind, Law is expecting the rivals to contest the destination of the Premier League trophy for the foreseeable future.
"Football now is a global game and it's really good for the city of Manchester to be shown throughout the world," Law told the London Evening Standard.
"We're back to the sixties when it was City and United. For the next few years, they will be the two teams that the rest of the country will have to beat if they want to win titles.
"Chelsea, Arsenal, Liverpool and Spurs, possibly, will have to be really good to beat the two Manchester teams."
Law represented both clubs during his playing career.