Doherty has made headlines in the tabloids for battling heroin addiction and spending two months in prison for burgling his now-estranged bandmate's flat.
This month, he was given a four-month suspended custodial sentence after pleading guilty to possession of a knife.
If he accepts the offer, he is likely to bring real controversy to the show, which in turn will pull in the viewers.
Oasis's Liam Gallagher and Tim Burgess, the frontman from The Charlatans, have already turned down the offer to appear in the show, which is due to air in a primetime slot next year.
Programme makers, Endemol, which makes 'Big Brother' proper and 'The Farm' for Five, has warned that the new show will have some surprising twists and turns for the celebrities.
The first 'Celebrity Big Brother' was a ratings success for Channel 4 with chatshow host Vanessa Feltz notoriously losing the plot and comedian and overall winner Jack Dee entertaining the nation with his humorous escape bids.
The second series also fared well, with former Take That boy band member Mark Owen winning the show, with former Page-3 model Melinda Messenger and drum-and-bass DJ Goldie among the contestants.
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