Turner, 27, played 17 times during an emergency loan spell at Deepdale last season - and North End manager Brown is keen for him to return after he rejected a contract extension from the Toffees.
Brown said: "Andrew Lonergan has been at the club for a long time, and we've discussed it at length that it might be time for him to move on.
"Therefore we need to bring in another goalkeeper and Iain Turner is at the head of that priority list. Iain went into talks about a further contract with Everton and came out of there of the firm opinion that he wants to play regular first-team football.
"It's a balancing act - we can't afford to carry both Iain Turner and Andrew Lonergan on the books in League One. It might be a case of Iain having to wait until Andrew decides to sign for someone else - it's a waiting game."