Britain's Commission for Racial Equality (CRE) and other critics have objected to chief constables proposing the introduction of quotas and use of "affirmative action" to tackle the chronic under-representation of non-white officers.
The CRE and others have said that this move could be politically explosive and divisive, inflaming community tensions.
Just 3.7 per cent of police officers in England and Wales are from the ethnic minorities, below the 4 per cent target that forces were supposed to have achieved two years ago.
The Government has said the police must meet a "demanding but realistic" 7 per cent target for 2009, but the Association of Chief Police Officers (Acpo) warned that it would not be hit until 2020.
Acpo said the Government would have to sweep away the ban on positive discrimination to produce a "truly representative workforce within the next decade."
Peter Fahy, the Chief Constable of Cheshire, said: "Chief constables believe there should be a debate on the future of employment targets and the case for changing the law to enable forces to employ the people they need and reflect the communities they serve." He said lessons had been learnt from the Police Service of Northern Ireland, where such action had been taken to boost the number of Catholic officers.
According to The Independent, there are 5,236 black and Asian officers in the 43 forces in England and Wales at the end of March 2006, a rise of 238 over the year.
A Commission for Racial Equality spokesperson said: "These forms of 'reverse discrimination' could actually increase community tensions, rather than ease them.
The police ought to stop hiding behind the smokescreen of 'affirmative action' and start looking at the real reasons why ethnic minorities are not applying."
Nick Herbert, the shadow Police minister, said: "Greater efforts need to be made to encourage black and ethnic minority candidates to join the police. But positive discrimination or affirmative action would be the wrong course - it would be divisive and counter-productive, potentially increasing racial tension."
The Police Federation, which represents officers, said it was shameful that Acpo should consider such a "crackpot idea".