Geordie Shore star Charlotte Crosby and model Sophie Anderton are also said to have agreed deals with Channel 5 for the latest series, according to The Sun.
Crosby and Atkinson have apparently accepted deals worth nearly six figures, while Anderton has agreed a £30,000 contract.
Former Manchester United manager Atkinson quit ITV as a pundit in 2004 after making racist comments on live TV when he thought his microphone was switched off.
Anderton - who has previously appeared on both I'm A Celebrity... Get Me Out of Here! and Love Island - was previously addicted to cocaine at the height of her career but has been clean for over three years.
Charlotte Crosby is quoted as saying: "We have cameras filming us 24/7 [on Geordie Shore], so I think Big Brother will be a walk in the park."
A Channel 5 spokesman