The Birmingham Mail reports the 45-year-old is a leading candidate to land the top job at the Hawthorns.
The Baggies are searching for a new boss after Sam Allardyce departed following relegation from the Premier League.
Appleton's one of the front-runners to land the West Brom role. He previously worked as head coach of the club's under-23s before taking over as Lincoln manager in September 2019 – succeeding current Pompey chief Danny Cowley.
The ex-Oxford supremo has done a fine job at Sincil Bank. In the 2020-21 season, the Imps punched well above their weight to reach the League One play-off final, only to be beaten by Blackpool at Wembley.
Appleton’s eye-catching work carried out at Lincoln has seemingly caught the eye of his former employers.
As things stand, he is currently the even-money favourite to land the West Brom job. The likes of Chris Wilder and Frank Lampard have also been linked.
It certainly would be a blow to Pompey's third-tier rivals if Appleton were to depart Sincil Bank.
Lincoln were expected to again challenge or promotion next season with Appleton at the helm.
Appleton spent a year in charge at Fratton Park before leaving for Blackpool in November 2012.