Pep Guardiola's side were one of the biggest spenders in England's top flight during the summer, having spent around £205m on five new faces.
As it stands, the two Manchester clubs have identical records in the league following four wins, one draw and zero defeats.
"Man City have spent the biggest amount in the Premier League so they are the principle contenders for the title," ESPN quotes Herrera as saying. "We will try to be there as well, we have quality as well, and we will fight for every title, but I think because of the money they have spent they are the favourites.
"There is always pressure when you spend a lot, but there is also pressure on us because we are the biggest club in England. We won three titles last season and City didn't win anything. They are under pressure. They need titles. But you know when you play for Man United, winning is an expectation and an obligation - but I like that obligation, to be honest."
The neighbours will not meet in the league until December 9, when United play host at Old Trafford.