PNE sacked Alex Neil on March 21 after a poor run of results and placed Frankie McAvoy in interim charge until the end of the season.
McAvoy is high up in the betting having started his tenure with a draw, win and defeat but Wycombe Wanderers boss Gareth Ainsworth is back as favourite.
Here are the latest odds from Sky Bet.
5. Uwe Rosler - 8/1
The ex-Brentford, Wigan and Fleetwood boss is currently head coach of German side Fortuna Düsseldorf. Was in the running for the PNE job when Alex Neil landed it in 2017. Photo: Camaerasport
6. Joey Barton - 12/1
The Bristol Rovers boss was briefly favourite although looks very much an outside bet. Photo: Camerasport
7. Grant McCann - 16/1
The Hull City manager had his turn at the top of the betting but his odds have lengthened of late. Photo: Press Association
8. Michael Appleton - 20/1
The former PNE midfielder has been in the mix from the start but has dropped back lately. He's trying to keep Lincoln in the League One play-off race at the moment. Photo: Camerasport