Any move to the Premier League side would be subject to Gloster obtaining a U.K. work permit.
Gloster, 20, is in a training camp for the U.S. U23 team ahead of the Olympic qualifying tournament scheduled to take place in March. He has been playing with PSV's reserve team for the past two seasons making six appearances and one start this campaign after making 16 appearances in the 2019-20 season.
Gloster signed with PSV back in August of 2019 after spending parts of two seasons with German side Hannover 96.
Newcastle has utilized Jamal Lewis at left-back for parts of this season, but since joining in September he has been a disappointment, failing to have much of an impact on either side of the ball.
Another option, Paul Dummett, has only recently returned from a long-term hamstring injury. Matt Ritchie has also been utilized. If Gloster does make the move, he would likely start out in the Magpies' reserve team.
Gloster has been mainstay for the U.S. youth national teams at both U17 and U20 level. He was part of the U-20 side that reached the quarterfinals at the 2019 U20 World Cup, starting all five matches for the Americans.