The Black Cats have been strongly linked with a move for the England international and Roy Keane and chairman Niall Quinn have now decided to firm up their interest.
Everton and Birmingham have also been linked with the highly-rated youngster, but it is Sunderland who have made the first decisive step in attempting to secure Nugent's signature.
However, the striker is currently on England duty at the European Under 21 Championship and Preston believe his future is unlikely to be resolved until he returns from Holland.
The value of Sunderland's offer has so far been undisclosed, but Nugent has been rated in the £7million bracket after scoring on his international debut against Andorra in March.