Unless he's selected as a captain's choice, Patrick Reed will likely not be representing his country at the Ryder Cup. He currently sits outside the top 25, in 33rd place on the points table right now, so he's not really on the radar. A captain's choice can be anyone eligible, but Reed is well behind most Americans right now.
This is because LIV Golf events do not get Ryder Cup or OWGR points. He can only earn points in Majors right now, and he hasn't performed as well as would have been needed to get into range of the tournament. Reed has a 7-3-2 all-time record across three Ryder Cups and is unbeaten in singles. However, he hasn't played since 2018.
This is disappointing to the golf star, who said before LIV Golf Dallas (via NUCLR GOLF on X):
“It's always on your mind. Anytime I get to represent our country, it means a lot to me. For me personally, I'm always thinking about trying to make every team."
He went on:
"Obviously, being a part of LIV where we don't get points, it's an uphill battle, but really for me it's focused on playing some great golf and having a chance. It's really going to come down to the Open Championship, having a chance to win there. You have a really good showing and play well there, then you just never know."
Patrick Reed said he has one more chance to "win the Open" and get into the tournament on his own, but he faces a steep climb to do that. All he can do, though, is "go out and give all" he has in an effort to make the team.
Can Patrick Reed get into the Ryder Cup?
LIV Golf members are not prohibited from playing in the Ryder Cup for Team USA or Europe. It's a little harder for the Europeans who must maintain a membership on the European Tour, which is hard given the opposition to LIV.

However, they're not barred. Bryson DeChambeau, who is currently fifth in Ryder Cup points thanks to his excellent Major performances, would make it if he stayed within that range. Even if he doesn't, he's likely to be picked as a captain's choice.
Keegan Bradley can pick six, not including DeChambeau, Justin Thomas, Russell Henley, Scottie Scheffler, Xander Schauffele, and J.J. Spaun. Those are the automatic qualifiers right now.
That means Reed would have to stand out above Collin Morikawa, Bradley himself, Maverick McNealy, Harris English, Sam Burns, Denny McCarthy, Brian Harman, Patrick Cantlay, Tony Finau, and Wyndham Clark to get picked. The American side isn't deep, but Patrick Reed may not be high on Bradley's list of potential candidates this year.