The move is a recommendation contained in a Construction Industry Training Board-sponsored report into the retention and career progression of Black and Asian people in the construction industry.
The report was launched on Wednesday at Rethinking Construction's Respect for People conference at the Cafe Royal in central London.
It suggests that site managers of main contractors should be responsible for meeting ethnic minority targets on test sites in London.
The report, written by researchers at Royal Holloway University, says: "A number of sites should be selected as a pilot group, whereby there is a target set, within the overall objectives of the site manager, relating to ethnic minority employment on site."
It adds that this would be in the London area and that the main contractor would need to acknowledge that this would require time and have an impact on the project's plan, timescale and resources.
One leading contractor, however, immediately criticised quotas as "unworkable" and said they could be damaging to race relations in the industry.
He said: "To have site managers determining the ethnic make-up of people working on sites is insane; there is no way this can be achieved when they are trying to make sure projects are on time and on budget."
The report recommends that the senior management in leading construction firms should demonstrate what action is being taken to address racial discrimination.
It goes on to say that guidance should be drawn up to allow construction recruitment agencies to report contractors that refuse to take on workers from ethnic minorities.
Speaking at the Respect for People conference, CITB chairman Sir Michael Latham said he was committed to achieving a more diverse workforce. He said: "We need a construction industry that looks more like Britain, and Britain is not all male and white. We cannot afford to ignore or marginalise 50% of the population."
The Royal Holloway report adds that the CITB should convene an implementation group that includes representatives from construction firms, client bodies, unions and education establishments to implement the recommendations.
It says main contractors and larger subcontractors should draw up guidance for site management on dealing with racial discrimination. Measures to prevent bullying on site should be "integrated into the core guidance they receive and not treated as an add-on".