According to sources, the film director is "thrilled" to be with Ainsley and eager to get married.
An insider told The Sun: "She's besotted with Guy and wants to marry him. And Guy seems thrilled to have found her. They see themselves growing old together.
"They are delighted he has met Jacqui. She's also getting on extremely well with the children [he had with ex Madonna] and that's been a deciding factor for Guy. It's only a matter of time before he proposes."
However, Ainsley is allegedly worried over what Madonna's reaction would be if they announced their engagement.
The source added: "Guy and Madonna have managed to stay close friends and Jacqui is worried about upsetting her. She can be pretty intimidating, especially when you start dating her former husband!"