Clarke was sacked on Saturday night after the Baggies' 1-0 defeat to Cardiff - their fourth defeat in a row which leaves them two points above the relegation zone.
Sky Sports understands West Brom do not have a successor in mind and that an appointment is not imminent.
Joint-assistant head coach Keith Downing will assume control of first-team affairs while the club searches for a successor.
That search began on Sunday with Di Matteo, who spent almost two years in charge at The Hawthorns between 2009 and 2011, the favourite at 5-2 with Sky Bet ahead of ex-Fulham boss Martin Jol (4-1).
The man who oversaw the final straw as far as the West Brom board was concerned - Cardiff boss Malky Mackay - is down at 25-1.
Owen Coyle, recently sacked by Wigan, is down at 33-1 along with Ian Holloway, who left Crystal Palace earlier this season.