Roy Keane pulled out of the race to succeed Neil Lennon yesterday.
That now leaves Clarke, 50, as the bookies' odds-on favourite, although there is competition from former Cardiff boss Malky Mackay and Owen Coyle, who has not worked since being axed by Wigan last year.
Ex-Chelsea defender Clarke, a boyhood Celtic fan, but was put on gardening leave by West Brom last December after the Baggies won just three of their opening 16 games.
He was officially relieved of his duties five months later, despite having led the club to eighth place in the Barclays Premier League in his first season in charge.