Chief constables in England and Wales say employment laws need to be changed to help boost the recruitment of black and Asian officers.
The Home Office has said it would prefer to work with existing laws
The Association of Chief Police Officers says the changes are needed to ensure the police service hits Home Office targets for minority groups.
Under the plans for "affirmative action", women would also get priority in order to boost numbers.
Critics have branded the idea "reverse discrimination".
Acpo says raising the 3.7% of officers from ethnic minorities to the Home Office's 7% target by 2009 cannot be done without changing policy.
However, a change to employment law is not favoured by the Home Office.
Peter Fahy, chief constable of Cheshire, who speaks for Acpo on race and diversity and who presented a report on the issue to an Acpo council meeting in central London, called for a wider debate on amending the law.
"What is clear is that current employment law will not allow the police service to achieve the goal of a representative police force for many years and without such a change current employment targets would have to be abandoned," he said.
Having the confidence of "all sections of the community" was "absolutely critical" to protecting the public and ensuring that "justice can be delivered", he said.
Under the changes being considered, black and Asian recruits with the necessary qualifications would be fast-tracked, to meet quotas set by each force.
According to Acpo, the plans would represent "affirmative action", which it defines as the process of prioritising minorities once they have passed initial selection procedures.
Under such a plan, if two job candidates met the required standards, the candidate whose ethnicity is under-represented in the force would be selected.
Acpo says this differs from "positive discrimination", which it says means hiring minorities regardless of whether they are qualified for a job.
BBC home affairs correspondent Danny Shaw said the Home Office had indicated it would prefer to work within existing laws to increase the numbers from ethnic minorities applying to join the police.
The Metropolitan Police Commissioner, Sir Ian Blair, said recruitment from ethnic minorities in his force was close to 20% but he admitted the Met would not reach the 2009 target of 25% black & Asian officers in the workforce.
He said: "The only way to achieve it would be to sack white male officers."
Sir Ian said the target should have been based on the proportion of new recruits rather than on the entire workforce.
But Keith Jarrett, President of the National Black Police Association, said he supported the use of affirmative action.
He told the BBC: "If we look at Hounslow in London, it's a borough that is predominantly from a minority ethnic background.
"Now whilst my white colleagues are immensely qualified to do the job, I would put forward that Hounslow would be better served as a borough by a person from an Asian background, who has got culture in common with the local inhabitants, and perhaps speaks the same language."
Nick Timmings, an employment lawyer with London-based TMP solicitors, said the police needed to be "making the career more attractive to people from different backgrounds".
He said there was an "old boys' network" in the organisation who liked to go to the pub and added that this left out those who could not drink because of religious beliefs.
Nick Johnson, from the Commission for Racial Equality, said the better targeting of resources, promotional work and training and development were better ways of addressing under-representation.
"Picking someone simply because of the colour of their skin for a job is not something we would support," he said.
A spokeswoman added later: "These forms of 'reverse discrimination' could actually increase community tensions, rather than ease them."
A Home Office spokesman said that while progress had been made in recruiting special constables, police staff and police community support officers from minority ethnic groups, recruitment of police officers was "moving at a slower pace" and "remained a challenge".