The 33-year-old has been deemed surplus to requirements at Wolves after a year at Molineux.
Reports in the national media over the past few days have suggested the Preston-born shot-stopper is keen on a return to the North West.
The Lilywhites are in need of a goalkeeper to provide competition to Chris Maxwell after Anders Lindegaard was released at the end of the season.
But sources at Deepdale indicate Lonergan is not a target.
Having come through the ranks at Deepdale, Lonergan has also played for Leeds, where he was signed by current PNE boss Simon Grayson, Bolton Wanderers and Fulham.
He joined Wolves last summer but has found opportunities limited, making 11 Championship appearances including playing in the 0-0 draw against PNE at Deepdale back in November.
A more likely target could be Declan Rudd, who spent a season-and-a-half on loan with Preston from Norwich.
The 26-year-old has had his contract extended this summer, having spent the season with Charlton Athletic.
His future at Carrow Road is unclear though, after the Canaries signed Angus Gunn, son of club legend Bryan, on a season-long loan from Manchester City.
Norwich also have Northern Ireland international goalkeeper Michael McGovern on their books.
Whoever arrives will have a tough task shifting Maxwell as North End’s No.1, the Welshman arriving last summer with the more experienced Lindegaard widely expected to be first choice between the sticks.
The former Fleetwood man soon deposed the Dane though and started 38 of Preston’s 46 league games, signing an improved and extended contract in March which ties him to Deepdale until 2020.
Youngsters Mathew Hudson and Callum Roberts are also under contract for next season.