The Express & Star have reported Pardew will avoid the axe due to his side's encouraging performance in Saturday's 1-0 loss to Watford.
Albion were close to holding on for a point at Vicarage Road before Troy Deeney scored the winner with thirteen minutes remaining in the match.
After taking over from Tony Pulis in November, Pardew has won just one of his fifteen matches in charge of the Baggies.
It is also believed the lack of a quality alternative has convinced the club's Chinese owners to hold off on firing the Englishman.
West Brom are currently bottom of the Premier League table and are eight points from safety.