Under a scheme that has been trialled in Doncaster prison, contractors such as G4S and Serco will only receive their full fee if reconviction rates fall with a year of release by five per cent.
Other proposed changes include a crackdown on prisoners being allowed to watch subscription Sky television.
The Daily Telegraph disclosed last month that thousands of prisoners are allowed to watch pay-TV satellite television channels at the taxpayers' expense.
Ministers admitted in a Parliamentary answer nearly 3,000 prisoners in private prisons "were eligible to access subscription channels provided by British Sky Broadcasting".
Mr Cameron will also announce plans for a new criminal offence of possessing a handgun with intent to supply - with a maximum sentence of life imprisonment.
The move comes as David Cameron launches a new drive in an attempt to show the government is tough on crime, and that he is abandoning his old "hug a hoodie" stance on law and order.
The Prime Minister will make a speech this week in which he will claim the coalition is pursuing a twin-track approach - "retribution" on crime while also trying to rehabilitate offenders.
The speech will be seen as a key part of his fightback against the political setbacks which have recently hit his government.
Other measures are likely to include fines for prison bosses who fail to stop criminals re-offending after release, in a new "payment by results" system and an "element of punishment" in community sentences, which have been dismissed as a soft option.
"Cushy" regimes for prisoners will also come under attack while the custom of giving £46 cash to all inmates when they are freed from jail may go. Mr Cameron is likely to use his speech to unveil a new law and order slogan: Tough but intelligent.
He will argue: "Retribution is not a dirty word."
The move on handguns has already been called for by MPs on the Home Affairs Select Commitee and by the Association of Chief Police Officers.