The ballerina, 30, who is due to give birth in two months, was snapped with her growing bump in New York and looking at baby books, a gift from a friend.
Rolling Stones star Mick, 73, is on the road with the reformed band.
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A source said: “He’s increasingly very busy with new work commitments, but he has promised to visit the baby when it is born. He and Melanie have their own independent lives.
“She dreams of returning to her career as a ballerina, while Mick has been throwing himself into the Stones.
“He wants to be involved as much as possible in his child’s upbringing. He will support the child financially.
Mick wants to be involved as much as possible in his child’s upbringing
"He wants Melanie to live comfortably and has already paid for a luxury townhouse for her in New York.”
It reportedly cost £5million. They began dating in 2014 after his partner L’Wren Scott committed suicide.
He already has seven children from five different women.