The Guardian reports today that following their defeat to Aston Villa in Tuesday evening's playoff semi-final, West Brom are eyeing up the former Ireland worldwide as the permanent successor to Darren Moore.
The Championship playoff final will take place on Sunday, May 26.
Craig Dawson had drawn Albion level on aggregate to bring the game to extra-time, although Chris Brunt's 80th-minute sending-off meant that they spent most of the additional half an hour clinging on - only to lose in the shoot-out.
Conor Hourihane, Mile Jedinak, Jack Grealish and Tammy Abraham all scored their spot-kicks for Villa with the only miss coming from Albert Adomah, taking fourth, who blazed his penalty over the crossbar.
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Despite incessant pressure from the Villans, the hosts managed to hold on through extra-time and force a shootout.
Grealish is one of the best attacking players in the Championship, and the youngster was brilliant against West Brom.
"There's obviously a lot of luck involved but wow - we practise penalties, so I think I must've faced 100 a day the last few days", Steer said. Their second leg is on Wednesday, with Leeds protecting a 1-0 lead at their Elland Road home.
Villa missed out in the playoff final past year, losing 1-0 to Fulham and Grealish, who has been linked with a summer move to Tottenham, is keen to make amends in what could be his final game for the club.