The 'Strictly: It Takes Two' presenter is said to be in ''advanced negotiations'' to move from her Saturday afternoon slot to take the ''job of a lifetime'', which would make her the first woman to host both the Radio 1 and Radio 2 flagship morning programmes.
However, Zoe - who was left devastated when boyfriend Billy Yates took his own life last year - is said to have held back on signing the contract while she figures out how to make the position work alongside her family life in Brighton, where she lives with children Woody, 17, and eight-year-old Nelly, who she has with former spouse Norman Cook.
A source told The Sun newspaper: ''We are in advanced negotiations with Zoe to replace Chris. A contract hasn't been signed and her new pay hasn't yet been agreed...
''The offer is on the table if Zoe wants the gig. She's fully aware it's the job of a lifetime. For her, being the first woman to host both the Radio 1 and Radio 2 breakfast show is a massive deal.
''But it's been a tough year for her and she's got over Billy's passing by throwing herself into work. She's only just found the perfect balance, so this offer coming her way has shocked her. She'd love to do it but she's putting the family first.''
The news is said to have come as a shock to Sara Cox, who had spoken openly of her desire to take the job and move from her 10pm evening slot, but she's second choice if Zoe, 47, turns down the offer.
The source added: ''Zoe was our number one choice and has been offered the job. If Zoe turns it down it will be offered to Sara, guaranteeing there will be a female hosting our flagship radio show for the first time.''
Earlier this month, Chris revealed he is leaving BBC Radio 2's 'The Breakfast Show', which he's helmed for eight years after taking over from Sir Terry Wogan, at the end of the year, to return to his ''spiritual home'' of Virgin Radio.
He said in a statement: ''In many ways Virgin Radio is my spiritual home. I see nothing but exciting and groundbreaking opportunities ahead. In a medium that is changing so quickly on a daily basis, the potential for growth is unprecedented.
''Our plan is, to give it all we've got, see where we can get to and have the most possible fun along the way. It makes me smile every time I think about it.''
The broadcaster hosted Virgin's breakfast show from 1997 until 2001 when he was sacked by the Scottish Media Group, which bought the station in 2000, for ''breach of contract'' after he failed to turn up for work for the sixth day in succession.
The station, which Chris once owned, went on to be rebranded as Absolute Radio in 2008 before Virgin was given a new lease of life in 2016 when Sir Richard Branson relaunched Virgin Radio UK as a digital station.
Chris will front Virgin Radio UK's Breakfast Show from early next year.
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