The Magpies were keen on the highly-rated Greek international last season, and still covet him.
Newcastle are awaiting approval for a big money Saudi takeover, which could lead to an offer being made for Vlachodimos.
Benfica do not intend to sell the 26-year-old, the latest in a string of impressive shot-stoppers on their books.
Last year, Vlachodimos extended his Benfica contract until 2024 and has a prohibitive €60m release clause.
Since then, the German-born goalkeeper has impressed, conceding only 33 goals in 35 games in the 2019-20 season.