The England international has been strongly linked with a move to the Magpies since the Saudi-led takeover of the club was completed back in October.
It is now understood that he is close to becoming the club's first signing of the new era following the opening of the January transfer window, says the Daily Star.
Newcastle are reportedly in advanced talks with both Atletico and Trippier as they aim to complete the transfer in the coming days to boost their survival hopes.
Atletico fans now believe that Trippier has wished farewell to the club's supporters following their most recent match.
The Spanish champions beat Rayo Vallecano at home on Sunday and Trippier was seen applauding the fans after the match.
Before the game, Atletico coach Diego Simeone confirmed Newcastle had met Trippier's buyout clause.