Tony Pulis and Tim Sherwood are in talks with West Bromwich Albion about succeeding sacked manager Alan Irvine, according to reports in the British media on Tuesday.
West Brom announced on Monday that they had sacked Irvine after a run of seven defeats in nine matches that left the club in 16th place in the Premier League table, just a point above the relegation zone.
Pulis was named the Premier League's Manager of the Year for steering Crystal Palace away from relegation last season, but he left the club on the eve of the current campaign after falling out with chairman Steve Parish.
Sherwood, out of work since being sacked by Tottenham Hotspur in May, was interviewed by West Brom during the close season, only for the club to appoint Irvine as the successor to Spaniard Pepe Mel.
The BBC said that both Sherwood, 45, and 56-year-old Welshman Pulis were in talks with West Brom.
West Brom announced Irvine's departure in a statement that read: "Irvine leaves the club with immediate effect and has been placed on gardening leave."
The Midlands club explained that the decision had been taken with "regret but necessity" and added that they expected to name Irvine's replacement by the weekend.
Assistant head coach Rob Kelly will take charge of the team for their New Year's Day game at West Ham United.
Albion's technical director Terry Burton said: "We appointed Alan in the summer convinced that we had taken on one of the foremost coaches in the UK and nothing that has happened since then has altered our view.
"The individual progress of our players such as Craig Dawson and Saido Berahino are testament to that.
"Securing a sixth season in the Premier League is the over-riding target and sometimes unpleasant decisions have to be taken to serve that imperative.
"Alan has impressed everyone with his manner, dedication and diligence, but he knows that results have simply not been good enough."
Irvine, 56, was the second Premier League manager to be sacked this season following Neil Warnock's dismissal by Palace on Saturday.
Newcastle United manager Alan Pardew has been given permission to speak to Palace, where he spent four years as a player, about the vacancy at Selhurst Park.
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