Newey, considered the greatest Formula One technical mastermind of his generation, will be a free agent next year after Red Bull confirmed he is set to end his association with the team.
Hamilton, who is moving to Ferrari next season, was asked ahead of this weekend's Miami Grand Prix how much he would like Newey to make the switch too.
"Very much," Hamilton replied, before adding: "Adrian Newey has got such a great history and track record and he has done an amazing job through his career. With the knowledge he has he would be an amazing addition."
Hamilton added: "They (Ferrari) have got a great team and they are making huge progress and their car is quicker this year, but it would be a privilege to work with him.
"If I was to do a list of people I would like to work with then he (Newey) would absolutely be at the top of it. Any team would be fortunate to have the opportunity to work with him."
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