The rapper has apparently "put his own spin" on Winehouse's 2006 hit 'Back To Black' to commemorate the singer, who died aged 27 last month.
According to The Mirror, music industry insiders have described the song as 'something special'.
The source commented: "It's pretty emotive. It's Kanye singing from the heart - with synthesisers."
West is expected to debut his rendition of the song during a performance at the Moss Bros 160th anniversary celebrations in London.
It is one of several tributes Winehouse has received from her contemporaries.
Green Day have recorded a new track titled 'Amy', while Pete Doherty plans to dedicate his summer festival appearances to Winehouse, with whom he was close friends.
Watch the music video for Amy Winehouse's 'Back To Black' below: