The Daily Mirror says that the Chelsea footballer has asked her to 'come away with me' - and Cheryl, 27, is 'hugely intrigued' by Ashley's proposal.
The news comes less than a fortnight after it was reported that the couple is planning an exotic holiday together later this summer.
Sources say that she believes that taking Ashley up on his offer could end the 'circus' that is her life in the UK and help her get over her X Factor disaster.
One source close to the footballer, 30, told the Mirror: 'Ashley has told friends he sees his future abroad and he wants to persuade Cheryl to come with him.
'It all boils down to what Cheryl wants, but the early signs are she would be up for the idea.'
And a friend of the singer said that the main attraction of going abroad would be the anonymity she could enjoy.
The friend said: 'She's found living in the UK to be fraught especially with so much "negativity" towards her now.
'But abroad, she could lead her life at her own pace. That's appealing to say the least.'
The Chelsea star believes he has 'one last move' in him and has targeted Real Madrid or
European champions Barcelona as his destination – as long as he can persuade Cheryl to go and live abroad with him.
The pair first got together in 2004, married in 2006 and divorced in 2010.
The Mirror also says that Ashley is buying new rings for him and Cheryl – to signify "a new start" in their relationship.
However Cheryl's friends and family have been less supportive, urging her not to get back together with her former husband.
Ashley was infuriated by recent reports that he was seen 'cosying up' with a woman in LA while on holiday with friends.
Cheryl, meanwhile, is keeping a low profile after being sacked from US X Factor last month and is said to be eagerly awaiting Ashley's return.
Lots of celebs have secret homes to where they can escape the limelight. Click on the image below to see some of the secret hideways of the stars....
Celebrities who holiday with their exes