Everton boss Moyes has been chasing Nugent, who have scored 17 goals, for a season. The 22-year-old grew up a Toffees fan and would be keen on a move.
Nugent joined Preston from Bury in January 2005 for £100,000.
Preston boss Paul Simpson admitted: “I’d love to keep David here but the Premiership is the place to be.
“If he is going to go I would like it settled as soon as possible so I know how much money I have to strengthen the squad.”
