The Belfast Telegraph reported on Tuesday that O'Neill was a leading target for the club, who it said had spoken to the 47-year-old's representatives about the position.
"No, we are not aware of any approach," an Irish FA spokesman said.
O'Neill's stock has risen since taking Northern Ireland to Euro 2016, their first major tournament since 1986.
They are also in contention to reach the playoffs for next year's World Cup finals, lying second in Group C, five points behind Germany but ahead of the Czech Republic and Norway.
Norwich are on course to finish mid-table in the Championship following their relegation from the Premier League in 2016.
They have been without a permanent manager since sacking Alex Neil in March and will end the season under caretaker Alan Irvine.
Northern Ireland's next qualifier is against Azerbaijan on June 10.
(Reporting by Neil Robinson, editing by Ed Osmond)
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