The reports of them expecting their first child comes after sources told the Mail on Sunday's Charlotte Griffiths that they are keen to kick off the next step in their relationship, including moving in together and starting a family.
The apparently broody couple have reportedly received the blessing of Chloe's business mogul father Philip and mum Tina.
The sources told the publication: "Chloe wants to get pregnant right away. She's off the booze already.
"Her parents have recently done an unexpected U-turn on Jeremy, and are now embracing him as one of the Greens. They are resigned to the fact he'll be a part of their lives forever," it was continued.
Green and Meeks are said to have first set their eyes on each other at the Cannes Film Festival in May 2017, where the "Hot Felon" was modelling for Phillip Plein.
Passionate pictures of Meeks and Green surfaced during a sun-drenched luxury getaway in Turkey in July.
As he reportedly enjoys preparing for fatherhood yet again with Green, Meeks is also embroiled in ongoing divorce proceedings with estranged wife Melissa Meeks.
According to TMZ, Meeks agreed a child support deal with his estranged wife and he will pay her US$1000 a month for their son Jeremy Meeks Jr, 8, retroactive to November 1, 2017.
The website also revealed that the former lovebirds agreed to joint legal custody of their son.
This comes after Melissa Meeks revealed Meeks ditched the family for his modelling career, has only seen their son a total of 30 days in more than four months since they separated, and has not sent her any money to help take care of the boy.
Melissa Meeks' attorney Lisa Bloom told TMZ: "We are pleased that we were able to get Melissa child support in an amount 25 per cent above legal guidelines.'
Adding: "And the parties have worked together to come up with a reasonable child custody and visitation schedule, as parents should."
The website also revealed that Meeks and his estranged wife are trying to settle the divorce and avoid hashing it out in court.
She is mother to his biological child Jeremy Jr as well as Robert, 11, a son from a previous relationship.
She also has a daughter, 16-year-old Ellie, and has previously said that both stepchildren consider Meeks a father figure.
In September, Melissa Meeks opened up about her heartbreak as she sat down for an interview with Inside Edition.
"I was in shock. I didn't really know what to do" she revealed.
"It wasn't an easy pill to swallow. This is not anything I expected ... I felt hurt. I felt betrayed.
"I believed in him, I believed in us. I truly though this would have a happy ending. It didn't have a happy ending for me."
Melissa Meeks also revealed she stayed with Meeks throughout his prison stint in 2014, before she uncovered his affair last year.
Meeks shot to fame in 2014 when his mugshot was posted by the Stockton Police Department after he was arrested on weapons charges amid a gang sweep.
The model was handed a prison sentence of 27 months in connection with the incident.
