The controversial suggestion that an outside firm such as Group Four or Securicor could chase late payments is a sign of growing exasperation with the performance of the deeply unpopular agency.
A review has been ordered by Downing Street and is being carried out by senior officials within the CSA. The government has pulled back from announcing the measure in a White Paper due to be published next Wednesday, but radical changes are still on the cards if the agency's record does not improve.
The Inland Revenue has also been asked to consider taking over the job, but has resisted strongly. Its senior staff believe association with the ill-fated and deeply unpopular agency could taint their reputation for efficiency and fuel public suspicion of the taxman.
Mr Blair has said he believes the CSA has lost public confidence. He is understood to have asked for a radical review after seeing proposals to be published in next week's White Paper.
More than half of absent fathers are behind with their payments and about a third have failed to pay anything in the past three months. While the Inland Revenue collects about 90 per cent of the money due to it from non-PAYE tax payers, the CSA is struggling to meet a target of 70 per cent.
Six years after the agency was set up by the Conservative Government, the taxpayer still supports 1.8 million children whose fathers pay nothing towards their upbringing. Self-employed fathers are among the worst payers, with just 20 per cent paying the full amount they owe.
But despite growing pressure from Downing Street, the idea of "outsourcing" the collection side of the CSA has met with resistance from the Department of Social Security and unions.
Barry Reamsbottom, Joint General Secretary of the Public and Commercial Services Union, whose members include CSA workers, said the agency could be run more efficiently.
"The answer to the problems of the CSA is not to privatise it or hand it over to another Government department. The answer is to improve its management and to deal with the serious problems of morale," he said.
Low public esteem and low pay had led to a staff turn-over rate of 25 per cent a year, he said. A pay rise last year from pounds 7,200 to pounds 8,000 had brought front line clerical staff above the minimum wage, but many staff were still leaving after a few months.
Next week's White Paper will aim to increase levels of payment by making the system fairer. In future, absent fathers will be asked to pay 15 per cent of their earnings after tax if they have one child, 20 per cent if they have two and 25 per cent if they have three.
Fathers who have a second family will have their payments reduced by 15 per cent when their first child arrives, with further cuts to 20 per cent and 25 per cent on the birth of a second or third.Reuse content