The 27-year-old Chilean forward is the reported subject of an enormous offer from the Chinese Super League which would land him around £400,000 a week.
Former Chelsea player and coach Wilkins saw Brazilian midfielder Ramires depart Stamford Bridge for a big-money move to Jiangsu Suning in January and has urged Sanchez to avoid making a similar mistake.
"He's probably earning enough now for his life. He's not going to be able to spend all the money he has earned already one would have thought," the former Blues coach told the Premier League Daily podcast.
"At Chelsea, we lost Ramires to China at 28 years of age. The money was so important for him. You have to remember, these South American guys, where they come from is an impoverished background and they think they have to accumulate as much as they possibly can by the time their career is over.
"I thought Ramires leaving was a massive mistake and I think for Sanchez to go there would be a massive mistake. He can earn enough at Arsenal and I sincerely hope he stays in the Premier League because he is a joy to watch."
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