The former Manchester United players say their St. Michael's development would transform Jackson's Row near Manchester Town Hall.
Their Â£200m proposal includes a five-star hotel, apartments, offices and restaurants.
Plans are expected to be submitted to the city council later this year.
Giggs and Neville revealed details of their proposed development in July.
A synagogue would be rebuilt, but the 19th Century Sir Ralph Abercromby pub and the former Bootle Street police station would be demolished.
The online petition claims two tower blocks at the centre of the scheme "are grossly inappropriate to this location".
"They don't reflect, respond to or respect their surroundings," the petition continues. "They are in the wrong place, out of proportion and overwhelm everything around them, including the town hall, central library and both old and new buildings in the city centre."
Stretford resident Paul Moore, who has signed the petition, said: "I work and socialise in Manchester city centre and think the history and uniqueness of the city is being lost by these glass soulless towers. To demolish historic buildings to make way for these is a crime."
Matt Harby said: "I'm not opposed to the designs per se (I've seen a lot worse), but this is completely the wrong site for it."
Neville and Giggs were involved in the development of Hotel Football, near their former club's Old Trafford stadium.
They are also turning the former Manchester Stock Exchange into a luxury hotel.
Before renovation started earlier this year, they allowed homeless people to stay in the building.
More than 1,500 people have signed a petition against Gary Neville and Ryan Giggs' "grossly inappropriate" plans to redevelop part of central Manchester.