The 'Beez in the Trap' rapper unveiled the track on February 14 but complained earlier this month that the accompanying clip was "taking way too long".
In an interview with Capital FM, Minaj has since revealed that work on the 'Starships' video is now finished, and it should be released next week.
"It's officially done. There was just one tiny little thing I wanted to change, but I know at the beginning of next week you guys will see it," she explained. "It may be too saucy for TV."
'Starships' was one of the first tracks released from Minaj's sophomore album Pink Friday: Roman Reloaded, which has also seen 'Beez in the Trap', 'Stupid Hoe' and 'Right By Your Side' with Chris Brown gain airtime.
Minaj returned to Twitter on Tuesday following an eight-day hiatus during which she deleted her account after a fallout with a fan.
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Watch Digital Spy's interview with Nicki Minaj below: