The 35-year-old popstar split from the 25-year-old singer earlier this year but they have remained cordial for the sake of their son Bear, 20 months, and she reportedly hopes they can spend Christmas together as a family.
A source told Closer magazine: ''Cheryl doesn't want either of them to spend Christmas apart from Bear. She thought that by inviting Liam it would bring them all together as a family.
''Liam's really grateful and hopes he can make it.''
Liam and Cheryl announced in July that they had ended their two-and-a-half-year romance.
They said in a statement posted to their respective Twitter accounts: ''We are sad to announce that we are going our separate ways. It's been a tough decision for us to make. We still have so much love for each other as a family. Bear is our world and we ask that you respect his privacy as we navigate our way through this together.''
Cheryl recently admitted that Liam ''maybe'' felt excluded when they had their son because she was consumed by a ''bubble of love'' for the little boy and had little time for anyone else.
She said: ''When I think back to the early days of new motherhood, I was in such a bubble of love, I actually don't think I saw anyone else.''
Asked if Liam felt excluded, she said: ''Maybe. Maybe.''
Liam had wanted children from the age of just 16 and was keen to ''settle down'' with Cheryl - but she suggested the reality wasn't what the 'Polaroid' singer had expected.
She said: ''He wanted to settle down and have a family and not do the solo thing.
''Then we encouraged him to do that. And then it didn't work out.''
Asked if it wasn't what he wanted after all, she simply replied: ''You'll have to ask him that.''
But the former Girls Aloud singer can understand why it was ''hard'' for Liam to juggle fatherhood with his solo career, while she took a break to be with the baby.
She said: ''He was almost having two lives. You have to switch your head onto pop star and then switch it back to daddy.''