The former Tottenham right-back is set to become the first signing of the Toon's new era under Saudi ownership.
Trippier, 31, waved goodbye to Atletico's supporters after their 2-0 victory over Rayo Vallecano on Sunday.
Boss Diego Simeone then confirmed that he wants to leave - with the deal nearing completion.
Simeone said: "We want him to stay - he's a very important player.
“But nowadays, when a player wants to leave, you can't force them to stay."
Newcastle are claimed to have matched Trippier's release clause, believed to be £31million, says The Sun.
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