The 52-year-old took over from Roberto Di Matteo after the Stamford Bridge side fell to a 3-0 defeat against Juventus to leave their Champions League hopes hanging by a thread.
However, while the Italian's replacement has picked up just two points from his first three games, Wilkins believes that Benitez will remain at the club until the end of the season.
Asked by BBC Radio 5 Live's 'Sportsweek' whether the former Liverpool boss could be dismissed early, he replied: "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.
"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."
The Blues were beaten by London rivals West Ham 3-1 on Saturday to leave fans furious but Wilkins feels that club owner Roman Abramovich needs to show patience with his managers as he is running out of options.
He continued: "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."
The 56-year-old suggested that former Chelsea midfielder, now Brighton boss, Gus Poyet would be a "good choice" for the permanent post, noting: "He is cutting his teeth at Brighton, he has been at Leeds and Swindon so he knows the trade and he is a Chelsea legend, as Roberto Di Matteo was."
Regardless of who is in charge, however, Wilkins is adamant that money must be spent in January to arrest the decline that sees the Blues 10 points off leaders Manchester City.
"Whether it is the club who spends money or Rafa who spends money, it has to be done because the season is coming to a rather rapid halt and we are not even at Christmas yet," he added.
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