Private security firms could investigate some crimes and patrol neighbourhoods under plans being drawn up for police in England and Wales.
The West Midlands and Surrey forces have invited bids for contracts from private firms, on behalf of all forces.
Staff would support officers carry out duties but would not make arrests.
Shadow home secretary Yvette Cooper said she was "very worried" at the pressure police are under to "cross the line" because of government cuts.
"The police have today confirmed that they are pursuing these contracts as a result of the financial pressures they face," she said.
"Yet the possibility of including the management of high-risk individuals, patrolling public places or pursuing criminal investigations in large private sector contracts rather than core professional policing raises very serious concerns."
Chairman of the Commons' Home Affairs Select Committee Keith Vaz said he was worried about some of the potential implications.
"Britain's policing is founded on accountability to the public,'" he said.
"Plans to privatise its frontline, particularly on the eve of the election of police and crime commissioners, is a cause for concern."
The Police Federation has also expressed fears about the proposal.
"This is an extremely dangerous road to take," said vice-chairman Simon Reed.
"The priority of private companies within policing will be profit and not people, and we must not forget, they are answerable to their shareholders and not to to the public we serve.
"This is not a solution. Chief officers must no longer bury their heads in the sand; they should instead stand up for what is right for the public and protect the police service from any further dismantling by this government."
BBC political correspondent Louise Stewart said the West Midlands and Surrey forces had been working together since early last year.
This is the first time the extent of their plans to involve the private sector in "middle and back office functions" have become clear.
They emerge at a time of 20% cuts to police budgets over four years, with Home Secretary Theresa May suggesting forces could protect "front-line policing" by delegating some work to the private sector.
Our correspondent says the two forces have invited bids from firms including G4S, the world's largest security firm, to deliver a number of services currently undertaken by the police.
They include responding to and investigating incidents, supporting victims and witnesses, managing high-risk individuals and patrolling neighbourhoods.
G4S already have a £200m contract with Lincolnshire Police under which half the force's civilian staff will join the private company, which will also build and run a police station.
In a statement, the Home Office said of the plans: "Private companies will not be able to arrest suspects, and they will not be solely responsible for investigating crime."
The contract has a potential value of £1.5bn over seven years but could rise to £3.5bn, depending on how many other forces signed up, our correspondent adds.
That would make it the largest contract to date for a private company to provide police services.
Chief Superintendent Phil Kay of West Midlands Police said the most important duties would still be carried out by sworn officers.
"Some elements of patrolling it may be appropriate, but the majority of patrolling, the majority of responding to calls for service, particularly 999 calls, will continue to be done by police officers,'" he said.
The Guardian reported it had seen a briefing note sent to companies on the West Midlands-Surrey plans, which said that all services that "can be legally delegated to the private sector" were potentially up for contract.
A West Midlands police authority spokesman told the newspaper the aim was to transform the way the force worked.
"The areas of service listed in this notice are deliberately broad to allow the force to explore the skills, expertise and solutions a partnership could bring," he said.
But Ben Priestley, Unison's national officer for police and justice, told the Guardian: "Bringing the private sector into policing is a dangerous experiment with local safety and taxpayers' money.
"We are urging police authorities not to fall into the trap of thinking the private sector is the answer to the coalition's cuts."
He added: "Privatisation means that the police will be less accountable to the public. And people will no longer be able to go to the Independent Police Complaints Commission if they have a problem."