The Baggies sit eight points from safety at the bottom of the Premier League table and have lost seven consecutive games in all competitions.
West Brom have now failed to take any points from the last 18 on offer in the top flight, and Pardew admitted after Saturday's 4-1 loss to Leicester City that his future at the club is increasingly uncertain.
According to Sky Sports News, however, Albion's decision makers do not think that sacking Pardew right now would improve their chances of staying in the Premier League and, as well as being costly, they feel that twisting may hamper the process of deciding who can best lead the team next season.
The report also claims that a number of possible candidates are thought to be unwilling to take over at The Hawthorns with the team so far adrift of safety at the foot of the table, while Baggies chief executive Mark Jenkins has not been instructed to make changes to the coaching structure or personnel by the club's owners in China.
West Brom last lost six Premier League games in a row in 2002-03, when they were relegated from the top flight.