The Blues are without a win in three Premier League games under the Spaniard following a 3-1 loss to West Ham United at Upton Park on Saturday.
Chelsea supporters continued to voice their dissatisfaction at Roberto Di Matteo’s sacking and Benítez’s appointment as the Italian’s replacement in the London derby.
But Wilkins, who spent six years at Stamford Bridge as a player, believes Roman Abramovich will stick with the Spaniard until the end of the Premier League campaign.
“I would think that is totally out of the question – they have asked him to come in and do a job and no doubt he is trying to work very hard to do it.” Wilkins told BBC Sport.
“Unfortunately the results are going against him at the moment. It has been a very difficult period for Chelsea and at the moment they are struggling.”
He added: “If Pep Guardiola was to come in and was sacked then where do you go?
“He is supposedly the best on the planet. He is a young man of 41. You have Mourinho out there but would Jose come back? I have no idea.
“The options are now being closed down rather rapidly.”
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news