West Brom are in talks with Tony Pulis and Tim Sherwood about their vacant manager's job.
The news comes after Albion sacked Alan Irvine, 56, on Monday with the club 16th in the Premier League.
Ex-Spurs manager Sherwood, 45, was interviewed for the West Brom manager's job before Irvine was appointed in June 2014 to replace Spaniard Pepe Mel.
Pulis, 56, guided Crystal Palace to Premier League safety last season before leaving that role in August.
He took over at Selhurst Park in November 2013 with the Eagles in the bottom three, but took Palace to a finishing position of 11th, 12 points above the relegation zone.
However, Pulis left before the start of the season as he did not want to work under a structure that saw Palace chairman Steve Parish and then sporting director Iain Moody take responsibility for transfers.
It is understood Pulis will only consider taking the West Brom position if he is given control of transfers.
West Brom chairman Jeremy Peace's current approach sees technical director Terry Burton work with sporting director Richard Garlick to recruit players.
Former Stoke boss Pulis is prepared to work alongside Burton and Garlick, but wants the final say on whether to sign players.
Sherwood, who captained Blackburn to the Premier League title in 1994-95, spent five months in charge of Tottenham from December 2013 to May 2014 in his only other managerial job.
He was a candidate for the West Brom role in June, but the move broke down when he asked to bring in his own coaching staff.
Albion are a point above the relegation zone following Sunday's 2-0 defeat at Stoke, their seventh loss in nine games.
Rob Kelly, who was Irvine's assistant head coach, is scheduled to take charge of West Brom's first team, along with Keith Downing, for the Premier League game at West Ham on 1 January.
The Baggies then host Conference Premier side Gateshead in the third round of the FA Cup on 3 January.