Appleton has been in charge at Sincil Bank since September 2019, when he replaced Blues boss Danny Cowley following his move to Huddersfield.
That first season saw newly-promoted Lincoln finish 16th in the third tier, although the final table was decided on a point-per-game method because of coronavirus.
But last term they emerged as the division’s surprise package to claim fifth spot and secure a place in the play-offs.
The Imps’ promotion hopes were ended by Blackpool at Wembley.
But Appleton’s reputation soared again as a result – putting him in the frame to replace Sam Allardyce, who left the Baggies after their relegation from the Premier League.
Several named have been linked with the vacant Hawthorns job, including David Wagner and Chris Wilder.
However, neither candidate was appointed, leaving the door open for Appleton to return to a club he played for and coached.
Yet, now the former Pompey manager has apparently turned down a return as he choses to instead build on Lincoln’s impressive League One showing from last season.
Appleton moved to Fratton Park in November 2011 from West Brom.
He was in charge of Pompey for one season – a term that saw the Blues finish 22nd in the Championship.
Appleton left in November 2012 to join Blackpool with the Blues 17th in League One.