The 40-year-old rapper produced the 'Daytona' LP and paid $85,000 for the shocking image - which was secretly taken by Whitney's sister-in-law Tina Brown in 2006 but Whitney's family are not happy.
Damon Elliott, whose mother is Dionne Warwick, said he only heard about the planned use of the image when his daughter told him.
He explained to PEOPLE: ''She was frantic. She sent me this picture from the album cover and I immediately got sick to my stomach because it took me right back to six years ago.
''I was actually in shock because I'm in the music business.
''I've watched the train wreck happening, but I didn't think he'd go this far in invading someone's family privacy.
''To do something for a publicity stunt to sell records, it's absolutely disgusting. It hurt my family and my daughter. It's petty. It's tacky.''
Damon previously worked with Kanye on a Keyshia Cole song and wants the rapper to explain his decision to use the picture.
He said: ''I just want him to tell me why he did it. What is the creative side of this? What's the point? It shows no creativity.
''What were you thinking? Did you think this through? And if you did, why did you do this?Because you're hurting people. It knocked the wind out of me. When someone passes, you try to mourn and move on and remember the good times.
''Why are you going to pay $85,000 to bring something to the forefront?''
The original image was published 12 years ago by the National Enquirer - six years before Whitney's death from accidental drowning aged 48.
Speaking about the artwork on The Angie Martinez Show, Pusha-T said: ''He changed my artwork last night at 1am ... My phone rings. No caller ID. (He says), Hey, yeah, I think we should change the artwork. And I like this other artwork. And this other artwork is 85 grand.' I said, 'Hey, I don't want to pay for that and I wasn't even going to ask you to pay for that. We picked what we picked, it's here, it's ready' ... 'No, this is what people need to see to go along with this music. I'm gonna pay for that.' I say, 'You my man! You my man!' ''
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