Swiss centre back Schär's stunner got the Magpies off to a fine start on the opening day against Nottingham Forest, with his thunderous 20-yard drive setting Eddie Howe's side on their way to a 2-0 win at St. James' Park.
England international Trippier's effort, meanwhile, also came at St. James' Park, as his stunning free kick put United 3-1 up against Manchester City 54 minutes into what was a pulsating eventual 3-3 draw with the champions.
And Saint-Maximin's sensational volley against Wolves has also made the shortlist, as his last-minute intervention - struck first time from a high, dropping clearance - rescued a point for Newcastle.
The Magpies trio are up against Brentford's Bryan Mbeumo, Arsenal's Gabriel Jesus, Chelsea's Kalidou Koulibaly, Luis Diaz of Liverpool and William Saliba of Arsenal for the prize, with public voting set to open at 12pm on Thursday, 8th September.
United supporters can cast their vote by clicking here. Voting closes at 12pm on Monday, 12th September.