According to the News of the World, the pair have been on a string of dates and have even been filmed together at Andre's Surrey mansion for his ITV2 reality show The Next Chapter.
A source said: "Peter and Keisha love spending time with each other and there is real chemistry between them. But because of what they've been through, they're not rushing into things.
"[Ex-wife] Jordan's still very keen to be in contact with Peter and to know what's going on in his life. This will be a real shock to her."
They are said to be taking the new relationship slowly after both suffering public break-ups in the past.