The England international, 33, joined Newcastle from Spanish side Atletico Madrid for £12m in January 2022.
He was Newcastle's first signing since their Saudi Arabian-backed takeover, and the first under manager Eddie Howe.
Ex-Burnley and Spurs defender Trippier has made 62 Premier League appearances for the Magpies and has regularly captained Howe's side this season.
Earlier this month, Newcastle chief executive Darren Eales said the club may have to sell players in order to comply with the Premier League's profit and sustainability rules.
German champions Bayern are keen on signing a right-back in the January transfer window.
Trippier, who has 46 caps for England, has played all but two of Newcastle's 21 Premier League games this season, with Howe's side 10th.
Newcastle have had to deal with several key absences this season, with nine first-team players currently out through injury or illness.
The Brazil international, 27, is expected to return to action in May.