West Brom chiefs are already drawing up a shortlist of names to succeed Alan Pardew.
The Baggies want Pardew to soldier on until the summer before dumping him with relegation accepted.
The Mirror says names set to be under consideration include Solihull-born Graham Potter,42, of Swedish club Ostersunds.
Michael Appleton, Leicester's assistant manager and an ex-West Brom player and coach, is well regarded by Jenkins.
Brentford's Dean Smith and Aberdeen's ex-WBA midfielder Derek McInnes are all seen as other potential contenders for the summer.