Reports state that the Baggies have opened talks about the Frenchman heading to The Hawthorns, although it is understood that there have been no formal approach from the Midlands outfit as of yet.
Ismael, 45, has two years left on his deal at Oakwell and reportedly has a £2m buyout clause with Albion said to be willing to pay the fee after switching their attentions to Ismael after former Sheffield United manager Chris Wilder and ex-Huddersfield Town chief David Wagner ruled themselves out of the running.
The Reds chief had previously been mentioned as a contender for the vacant position at Albion, but was ruled out because of concerns over his style of football held by sporting and technical director Luke Dowling.
But Dowling's exit from the club by mutual consent has prompted a reappraisal of the credentials of Ismael, who is understood to be able to speak to clubs if they offer a set fee due to a release clause in his contract.
Ismael performed heroics at Oakwell last term in an outstanding 2020-21 Championship season which saw Barnsley swap a relegation fight last term for a promotion quest.
They bowed out of the Championship play-offs in the semi-finals after a narrow 2-1 loss to Swansea.
Speaking after the second leg in Swansea, the former LASK Linz head coach spoke about needing time to reflect before focusing on the future.
Ismael, whose sterling feats at Oakwell have seen him linked with other clubs including former side Crystal Palace and West Brom said: “We have time to prepare and see what is going on in the future. But at the minute, we will reflect on the season and we will see.
“I gave everything and now it is time to reflect on this. I want to thank everyone at the club and the staff for their commitment.
“They were all dedicated, the players, the background people and our fans for their support on Monday. We can be proud."