West Brom have asked Barnsley for permission to speak with their manager Valerien Ismael, the PA news agency understands.
The Baggies parted company with Sam Allardyce at the end of the season following relegation from the Premier League and Ismael is their leading choice to take over.
Ismael, 45, transformed Barnsley from Sky Bet Championship relegation favourites to promotion challengers in his first season at Oakwell.
The French-born former Crystal Palace defender, who now has German citizenship, led the Reds to an unlikely play-off spot before they were beaten by Swansea in the semi-finals.
West Brom chief executive Xu Ke – who is known as Ken – is leading the search for Allardyce's replacement following the departure of sporting and technical director Luke Dowling by mutual consent on Monday.
Allardyce was unable to save the Baggies from an immediate return to the Championship and suffered his first Premier League relegation in May.
The former England boss had replaced the sacked Slaven Bilic in December and although West Brom made him an offer to stay, Allardyce said he felt unable to commit to the club long term.
Former Sheffield United manager Chris Wilder was reported as the West Brom board's first choice replacement, but it is understood that was vetoed by club owner Guochuan Lai.
Ex-Huddersfield boss David Wagner was then linked to the vacancy before he was appointed last week as head coach of Swiss club Young Boys.
Lincoln manager and ex-West Brom midfielder Michael Appleton was another reported target, but he has stated his desire to remain at Sincil Bank.
Former LASK head coach Ismael took over at Barnsley in October last year after the club had failed to win any of their first seven Championship matches.
The Reds were 21st in the table, but proved to be one of the season's surprise packages and ended the campaign in fifth place.
Barnsley lost last month's play-off semi-final to Swansea 2-1 on aggregate.