In a statement on Sunday, the prime minister's office said Netanyahu had submitted a request for a pardon to the legal department of the Office of the President.
The president's office called it an "extraordinary request", carrying with it "significant implications".
Netanyahu is the only sitting prime minister in Israeli history to stand trial, after being charged with fraud, breach of trust and accepting bribes in three separate cases accusing him of exchanging favours with wealthy political supporters.
He has not yet been convicted of anything.
The request comes weeks after US President Donald Trump urged Israel to pardon Netanyahu.
In a videotaped statement, Netanyahu said the trial has divided the country and that a pardon would help restore national unity.
He also said the requirement that he appear in court three times a week was a distraction that made it difficult for him to lead the country.
Netanyahu's request consisted of two documents - a detailed letter signed by his lawyer and a letter signed by Netanyahu.
They'll be sent to the justice ministry for opinions and will then be transferred to the Legal Advisor in the Office of the President, which will formulate additional opinions for the president.
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