The 36-year-old cage fighter - who split from wife Katie Price after 11 months of marriage in January - and the reality TV star are eager to have kids immediately after Chantelle recently discovered she will need IVF (invitro-fertisliation) treatment and must conceive within the next three years if she wants to become a mother.
Alex said: "We have discussed having kids, of course we have. It's fast-forwarded things a bit. It's not the sort of conversation you normally have when you have only been together for four months. We haven't put any pressure on each other."
Chantelle added: "We haven't made any firm decision yet but in our hearts we both feel ready for kids. It would be a natural thing for us to have children together. But we have to take a reality check - we have been put in this situation by fate. Watch this space."
Despite the pressure to have children as soon as possible, Chantelle - who was told she would be unable to conceive naturally following years of crash dieting - doesn't feel it will adversely affect their relationship.
She told Britain's OK! magazine: "I don't feel like it is a massive pressure. Everything seems to be happening pretty naturally right now, which is great. It's not like we're dead young. Alex is late thirties and I'm late twenties. We're kind of ready for this now. I want to have children."
Alex - who has been dating Chantelle for four months - is no stranger to IVF as he and Katie unsuccessfully underwent the treatment during their marriage.
Gritty and involving, this small British thriller is like Memento crossed with The Bourne Identity...