The 34-year-old made just six Premier League appearances during the 2018/19 campaign and his deal is set to expire at the end of the month.
However, the Liverpool Echo reports that the Toffees want to hand him a one-year extension, with manager Marco Silva eager to use him as a back-up to first-choice left-back Lucas Digne.
Baines is yet to make a decision on his future and is currently in the USA on his end-of-season break as he considers his options.
According to the newspaper, a potential move north to join Steven Gerrard’s Rangers is not on the table and reports of interest from the Scottish Premiership club are incorrect.
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