The 51-year-old singer has hinted she is ready to settle down with her 22-year-old lover, even though they have been dating for less than a year.
She is quoted as saying: 'It can go either way. But why not? I could definitely see myself marrying him. Yes, it's definitely on the table.
'He's so sweet. He checks in with me all the time. I probably should do the same, but you know me. I think he gets it now that I'm a little, shall we say, self-involved.'
Madonna – who has been married twice, to actor Sean Penn and British film director Guy Ritchie – is considering a lavish wedding to show the world just how in love she is with the Brazilian model.
A relative of the pop legend said: 'She knows that's what Jesus wants. She has a lot of wonderful memories of both of her weddings. She doesn't want to slip off and do it quietly. She definitely wants a big and rather fantastic affair.'
Madonna began thinking of walking down the aisle again following the death of her friend Michael Jackson in June.
The loss of the 'Bad' singer – who died of acute Propofol intoxication – made her more determined to live her life to the full.
She is also keen to show the world she is serious about the relationship, especially as she knows some people have been surprised by her decision to date someone almost 30 years her junior.
A friend told this week's edition Britain's Hello! magazine: 'When Madonna and Jesus were just dating – back when she thought it was a fling – she was OK with it. But when she realised she was starting to have feelings for him, she started to become self-conscious about the relationship. 'I don't want my family to think I'm having a mid-life crisis, 'she told me. 'And my friends, too. I don't want people to think I have lost my mind.''