City have made a flying start to the Premier League season, unbeaten after 15 matches to be eight points clear of United atop the table.
Guardiola's men are favourites to add to their 2011-12 and 2013-14 successes this term but United legend Giggs – who won 13 Premier League titles during his time at Old Trafford – insisted the Red Devils are still number one in Manchester.
"No," Giggs told Sky Sports when asked if City are the biggest club in Manchester.
"There are more academy players coming through at United than there are at City. United won two trophies last year, and City haven't won any for a couple of years.
"They are obviously very good, and with the spending power that they have got, every year they get closer, but still United, with the record that they have got, to go with the top manager and the top players, are still on top, but the gap is closing.
"With that spending power, and the coach that they have got, they will be very difficult to stop them over the next couple of years, because they are playing unbelievable football.
"But until you win that trophy, you can't start comparing them to Arsenal's Invincibles or other teams who have won the Premier League."