Chief constables in England and Wales are to discuss whether to boost the recruitment of black and Asian officers by "affirmative action".
The Home Office has said it would prefer to work with existing laws
The Association of Chief Police Officers will debate the move, which would need employment law changes.
Under the plan, women would also get priority in order to boost numbers.
However, critics branded the idea "reverse discrimination" and suggested that the police should make itself more attractive to ethnic minorities.
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, is calling for a debate on amending the law.
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: "We have had clients who have worked in the police for a while and found the culture repellent.
"What the police need to be doing is make 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.
He added that changes in the law required to facilitate these ideas would have to be "fairly radical".
Nick Johnson, from the Commission for Racial Equality, said there were better ways of addressing the problem of under-representation.
He said: "Positive action is about going into certain communities, targeting resources, targeting promotional work, building up training and development - that's something we would support.
"Picking someone simply because of the colour of their skin for a job is not something we would support."
A spokeswoman added later: "These forms of 'reverse discrimination' could actually increase community tensions, rather than ease them."
'Fair and square'
British Transport Police officer Trina Allen told BBC News she did not feel she had been given special treatment when she had applied for her job.
She said: "I'd hate to think that I'd get my job because of my colour. I've been through the entire process and at no point there was anything hidden to say 'apply because you're black'."
Chaz Singh, who was turned down by the force, said it would not be right to get the job because of a person's colour.
"I didn't get the job fair and square. It didn't go any further than that," he said.
"But to turn round and now be received in the sense that I could apply for a job because of my colour, I think that's wrong. I don't think colour should come before ability."
Matt Powell, a white candidate who was awarded compensation from Gloucestershire Police after they rejected his application, has described Acpo's proposals as an "absolute disgrace".
"People want the best police force, and if you start ring-fencing jobs for certain groups, I think you're going down a very dangerous path," he said.