The 20-year-old Scottish international was a target for the Toffees in the summer, when they sent in two transfer bids to Rangers.
However, their offers were not deemed acceptable at the time.
According to The Guardian, Everton are set to renew their efforts to secure Patterson.
Manager Rafa Benitez wants to sign a right and left back to improve his team's defence.
The Toffees are close to securing left back Vitaliy Mykolenko from Dynamo Kyiv.
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