Former Norwich boss Neil was photographed at Deepdale and his odds shortened with the bookies to 1/20 to get the job.
North End sources said Neil being there was part of an ‘ongoing process’ and that nothing had yet been concluded.
But two promotions on his CV – he got Norwich to the Premier League and before that took Hamilton to the Scottish top-flight – have him close to getting it.
More than 30 people applied for the PNE manager’s vacancy, one created by Simon Grayson’s departure to Sunderland last week.
Neil had lengthy talks at Deepdale yesterday with Peter Ridsdale, advisor to PNE owner Trevor Hemmings.
The 36-year-old left Norwich in March after more than two years in post at Carrow Road.
When appointed by the East Anglia club in January 2015, he was the second youngest manager in the Football League.
That season, Neil guided the Canaries to promotion to the Premier League, with them beating Middlesbrough 2-0 in the Championship play-off final at Wembley.
Their victory came the day after PNE beat Swindon 4-0 in the League One play-offs.
Norwich stayed in the top flight for one season, with them relegated in May 2016.
The Canaries were eighth in the Championship when Norwich dismissed him in March.
North End hope to have a new man in place this week and by speaking to Neil, have set the ball rolling.
As a player, he started out at Airdrie before making a move to Barnsley – he scored for the Tykes against Preston at Deepdale in November 2001.
Neil then joined Mansfield before heading back north of the border to play for Hamilton.
It was at Hamilton where he got his first job as a manager, guiding them to promotion to the Scottish top-flight in his first season in charge.
PNE returned to pre-season training last Thursday, the day Grayson left to join Sunderland,
They play their first friendly against Bamber Bridge on Friday night before heading to a six-day training camp in Ireland.