Neil saw the Lilywhites win their third game on the bounce on Saturday, beating Huddersfield Town 3-1 at Deepdale with goals from Jayden Stockley, Alan Browne and Paul Gallagher.
Last week, the 38-year-old Scot was subject of a failed attempt by Stoke City to lure him to the Potteries, while West Bromwich Albion tried for him in April.
Interviewed by Colin Murray on Quest TV during their EFL highlights show, Neil said: "If you look at what the lads give me on the pitch, there is no way I could leave that.
"They leave nothing at the door, I feel really privileged to coach them.
"That is the main reason why I see my foreseeable future at Preston, leading this team and hopefully achieving something special."