The Hole singer was seen kissing Andre at the Mercer Hotel, in New York, and the pair are said to be an item again after splitting in May.
A source said: "They were all over each other."
The reunited couple are now planning to move to the UK together and want to buy a house in north-west London when Andre opens two new hotels in the British capital next year.
Andre, 56, is also trying to be a calming influence on 46-year-old Courtney - famed for her hellraising behaviour and past drug use -and has told her if they are going to be a couple she needs to turn her back on her wild ways.
A friend told The Mail on Sunday newspaper: "Andre flew Courtney to St. Tropez to meet his father in the summer. He calls her by her middle name Michelle and they often just spend nights in eating ice cream and watching movies. They feel very strongly about each other.
"But he has told Courtney that if it's going to work then she needs to clean up her act. She serious about this too and is even willing to end her rock 'n' roll lifestyle."
Andre - who owns the Chateau Marmont hotel in Los Angeles - was previously married to Ford Models heiress Katie Ford but they divorced in 2004. He then dated actress Uma Thurman for three years until separating from her in March 2007.
Courtney is famously the widow of Nirvana rocker Kurt Cobain - who committed suicide in 1994. She has an 18-year-old daughter Frances Bean from her relationship with Kurt.
Andre and Courtney broke up in May after Andre became angry at the rock star's need to talk publicly about their romance and her jealous behaviour.
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