David Wagner and Steve Cooper have joined Frank Lampard and Chris Wilder on West Bromwich Albion's shortlist of candidates to replace Sam Allardyce as head coach.
However, reports that Oxford United manager Karl Robinson is under consideration are wide of the mark.
Albion's bosses were impressed by the job Wagner did in getting Huddersfield promoted in 2017, and then keeping them in the Premier League the following season.
They would also avoid paying compensation, with Wagner out of work since leaving Schalke in September.
Cooper would be more costly, and he has avoided questions about his future while Swansea are still involved in the Championship play-offs.
They play Barnsley in the second leg of their semi final on Saturday, with a 1-0 lead from the first leg.
Cooper is also a contender for the Crystal Palace job, which will become vacant when Roy Hodgson leaves at the end of the season.
Fellow candidates Lampard and Wilder are currently available, having departed from jobs at Chelsea and Sheffield United during the season.
Allardyce will take charge of the already-relegated Baggies for the final time in Sunday's season-ending Premier League trip to Leeds.
He has refuted suggestions he opted to leave after failing to receive guarantees over the club's future direction - and insists the parting of the ways will be entirely amicable.