The goalkeeper and captain, whose contract expires next year, is expected to move to Bayern Munich in the summer.
But Rangnick said: "Whether Manuel Neuer really plays his last game - I would not be so sure."
Whatever the future holds for the Germany international, Rangnick insists the issue should not affect his players.
"It is not about winning the cup for one particular player," he added in Sport Bild.
"Everyone has to want to win it for himself."
Victory would provide at least a some cause for celebration in what has largely been a miserable season for the Royal Blues.
Reaching the Champions League semi-finals has barely helped mask an atrocious domestic campaign as they as they finished in 14th place in the Bundesliga, just four points above the bottom three.
The Gelsenkirchen outfit go into the game on the back of six straight losses in all competitions.
But the cup has proved a welcome distraction from their league form and only the team which came eighth in the 2.Bundesliga now stands between them and a European place.
"We are not scared. We are convinced that we will win the game if we produce our normal performance," Rangnick, who took over from Felix Magath in March, told a press conference.
Duisburg are looking to make Schalke their third top-flight scalp of the competition, having already knocked out Kaiserslautern and Cologne.
And midfield Ivica Grlic believes, with Schalke such clear favourites, his side have nothing to lose.
"Our chance lies in the fact that this is a one-off game of 90 or 120 minutes," he said.
"Because it's very clear who the favourites are, we can actually play with freedom."