Madonna has written a song for Guy Ritchie calling him her "eternal love".

The singer - who divorced the British film director earlier this year after almost eight years of marriage - penned a track about a couple who loved, fought and loved again, sparking speculation the pair are set to reconcile.

Madonna has even ordered Guy a special personalised rifle for his birthday in September.

A source told Britain's Grazia magazine: "The whole relationship now is just unbelievable. Not long ago, people wouldn't even dare bring up his name because it was so bad. When they did talk, all they did was scream abuse at each other down the phone.

"Madonna has met few people in her life she truly respects and one of them is Guy. Forgetting everything else, she admires his intellect and cares about what he thinks.

"No one ever expected they could go from lovers to enemies and then back to incredibly close friends."

Friends of the 'Sherlock Holmes' filmmaker have also claimed he still refers to Madonna as if they are married.

One source said: "He'll often say, 'My wife is in great shape.' "

The couple agreed to resolve their differences after Madonna's 12-year-old daughter Lourdes from a previous relationship told her mother she wanted the pair to get along.

A source said: "She sat down with her mother and told her straight out that she wanted things to be good. It was then Madonna who called Guy and they met up in London and spent hours just talking. There was no shouting, no attitude and no hostility."

The former couple - who also have sons Rocco, eight, and David, three, together - have further strengthened their bond since the singer introduced Guy to her newly-adopted daughter Mercy, four.

The source added: "They have spent time together as a family, it was all very low key. He and Madonna were laughing together, he was teasing her like he used to and The Edge was gone. She was asking him a lot of advice and getting him involved in decisions."