Bedfordshire, Cambridgeshire and Hertfordshire have said that they plan to continue developing a business case that will consider outsourcing the services to G4S, which include IT and human resources.
The forces are analysing a contract in order to "assess the ability of the contract to meet the specific requirements of Bedfordshire, Cambridgeshire and Hertfordshire".
A statement released by the authorities said: "The full business case will therefore be completed over the next few months, ready for consideration and a decision by the Chief Constables in conjunction with the incoming Police and Crime Commissioners."
in July that problems with the company's scheduling system was partly to blame for the shortfall of over 3,000 security staff for the Games.
Speaking at a parliamentary committee meeting, Buckles told MPs that he got a call from the group's COO, David Taylor Smith, on 3 July, while he was on holiday in the US, citing problems with the company's rostering software.
Labour's MP for Luton South, in Bedfordshire, has said that G4S should not be considered for the contract.
Gavin Shuker said in a blog: "Put simply, our police shouldn't be privatised. It's the wrong response to a terrible decision - a choice made by this government to slash our policing budget."
He added: "Just as with the Olympics, the private company takes all of the reward, while taxpayers take all the risk. In the case of the games, the army had to step in. But who will protect us if a similar deal with Bedfordshire Police falls short?"
However, research director at , Sarah Burnett, told Computerworld UK that G4S can't be judged because of its poor performance over the summer when looking at IT outsourcing.
"Comparing the three police forces' requirements with the Olympics security debacle is like comparing apples with pears. The Olympics requirement was for a large number of people to supply services for a very short time. As I understand it was designed to work on 'just in time' principles but it failed spectacularly," she said.
"The three police forces are looking at transformational outsourcing offered as part of a framework that runs for 10 years. They are doing a business case and so are clearly examining all the options that they have for saving £73m in costs."
She added: "These types of long-term transformational deals require strong management and buyers have options. They can reduce risks by having exit clauses and termination strategies. Different types of pricing can also be negotiated. At Lincolnshire Police G4S has underwritten the £20m or so savings."