Speaking two days before the start of the biennial event against an International team, Stricker said his players would follow the usual protocol if they are present when the anthem is sung before the first match on Thursday.
"We've had a discussion already and none of my players want to do that (protest)," he told a news conference at Liberty National Golf Club, within sight of the Statue of Liberty.
"I just wanted to know what they wanted to do and how we wanted to proceed as a team.
"So we were going to do what we wanted to do and that's take off our hat and put our hands across our chest and over our heart and respect the flag."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
In a gesture initiated last season by then-San Francisco 49ers quarterback Colin Kaepernick, several NFL players have routinely "taken one knee" during the playing of the anthem.
It is intended to call attention to what the protesting players see as a pattern of racism in the treatment of African-Americans by U.S. police.
The issue has been magnified since U.S. President Donald Trump last Friday said any NFL player who protested during the anthem was a "son of a bitch" who should be fired.
Trump on Tuesday called for the NFL to ban any player who knelt during the anthem.
The generally conservative world of professional golf has steered clear of the controversy.
At the Presidents Cup, the players might not even be present during the brief ceremony before the first match on Thursday, when singer-songwriter Darius Rucker will sing the U.S. national anthem.
"We talked about it on the bus today," said Stricker, who added that he deferred to his 12 players.
"It was up to them ... We all realise there are some things going on in the world that aren't right.
"We want to show our support for the flag and it (acknowledging the anthem) gives us the opportunity to come together as a team."
U.S. assistant captain Davis Love said on Tuesday that he did not approve of anthem protests, while American team veteran Phil Mickelson trod a diplomatic line.
"We have social injustices in this country and we should all strive to eliminate them," Mickelson said as he prepared for his 12th consecutive Presidents Cup appearance.
"We've made great strides over the years but we've got a ways to go, and we should all strive to eliminate those.
"But this week, I'm so proud to represent the United States, to play for my country, to play for my team mates and participate in this great event.
"I don't know what else to add."
(Reporting by Andrew Both; Editing by Toby Davis and Ken Ferris)
