Council leaders have visited other authorities which have also outsourced many of their service to private firms.
Councillors were shown how the scheme works at Southampton City Council – which has signed a 10-year, £290million contract with Capit
a - as well as South Oxfordshire District Council.
Havant council – which provides services such as housing, planning, refuse collection on Hayling and runs Beachlands and the Island's public car parks - is looking into taking on Capita in a bid to save up to £2.6million from its budget.
The eight-year contract would mean some of the council's core services – including customer services, finance and property – would be carried out by the firm.
Other affected departments include design print and mail, payroll, support services and IT.
A report to councillors says Capita would look to save £7.1million on what it currently costs the council to do the work by running services more efficiently.
However, union officials fear it could lead to job losses and lack of control over the council's functions.
Council leader Tony Briggs said it was far from a "done deal."
The Conservative said: "In deciding whether or not a bid is right for the area then we normally visit other authorities who are using that company to get their view.
"No decision will be made for at least another couple of months until we have the final bid, all the evidence and are in a position to make a reasonable judgement."
He added: "It's rather like going out to buy a new car. You test drive it before you buy it. It's the same thing.
"Is it suitable for the purpose you require?"
Mike Wilson, regional organiser for Unison, which is opposing the move, said: "We are quietly lobbying behind the scenes and will see what proposals come out and act appropriately.
"We believe in public services delivered by a directly employed workforce. We don't see a place for private profits in public service.
"There's no conclusive evidence that private organisations can deliver better public services."
As the Islander reported back in January when the move was first mooted, Capita already processes benefits and revenue at an office suite at Havant's civic centre.
Capita Group Plc is the country's biggest back office firm and carries out administrative tasks for thousands of organizations - both in the public and private sector.
In 2006 it reported an 18 per cent rise in full-year pre-tax profits, rising to £193.2million.
It also administers the London congestion charge, manages more than 15million savings, pension and life policies and collects more than £3billion in TV licence fees each year.
It advises more than 300 local authorities on their debt portfolios.
