Benitez has endured a horrid start, with two draws and then a first defeat coming away to West Ham on Saturday.
The Spaniard, who played his part in a fierce rivalry with Chelsea while he was manager of Liverpool from 2004 to 2010, was already an exceptionally unpopular appointment by Blues owner Roman Abramovich at the end of last month. But Wilkins says he will be allowed time to improve results.
“I would think that is totally out of the question,” Wilkins said, when asked about the possibility of Benitez losing his job.
“They have asked him to come in and do a job and no doubt he is trying to work very hard to do it.”
Russian billionaire Abramovich fired Chelsea’s fan-favourite manager and ex-player Roberto Di Matteo last month and is running out of candidates to be a long-term replacement, Wilkins added.
“The options are now being closed down rather rapidly,” he said, naming ex-player Gus Poyet as a possible, popular choice.