Wicketkeeper-batter Buttler stepped down from the role on February 28th, three days after England's group-stage exit at the Champions Trophy, with Harry Brook considered a front-runner to replace him.
Asked if he would be interested in taking over the vacant role, Duckett told Sky Sports: "To captain England would obviously be a dream. I don't think it's on the radar, but I don't know that, which is why I am answering like that.
"We will see what happens moving forward and what decisions are made. I am just pretty happy playing for England at the minute.
"Three or four years ago I wouldn't have thought I'd be doing that, so just living my dream as a kid, representing my country - I am very happy playing all three formats."
The 30-year-old has played 22 ODIs and 17 Twenty20 Internationals, scoring 1,058 and 412 runs, respectively. He has also played in 32 tests, scoring 2,270 runs.