Brees knew Sunday night that he needed surgery for ligament damage, sources told ESPN's Chris Mortensen. The quarterback was still deciding who would do the surgery and when.
Brees said he will meet with Dr. Tom Hunt in Houston on Tuesday morning for a second opinion.
"I am evaluating my options and will make the best decision very soon," Brees said.
Saints coach Sean Payton declined to answer "hypothetical" questions about Brees not playing, saying, "We'll have a plan either way." But when asked if the Saints have built a team that could withstand Brees' absence, Payton said, "Well, we're getting ready to find out.
"Hopefully the news is good and the length of time, if there is any, that he's out will be shorter than longer. But that's part of our sport," said Payton, who said this kind of adversity is "kind of the nature of our league sometimes."
The Saints have not indicated whether they will consider placing Brees on injured reserve, which would free up a roster spot but would require the quarterback to miss at least eight weeks.
New Orleans will turn to Teddy Bridgewater, who is the NFL's highest-paid backup quarterback on a one-year, $7.25 million deal.
Brees had his right thumb and lower hand/wrist area taped by a trainer on the bench and remained on the sideline for the rest of the game in uniform.
After the game, he acknowledged that he was "concerned" about the severity of the injury.
With Brees likely to miss multiple games, the Saints are now 25-1 to win the Super Bowl at Caesars Sportsbook. Prior to Sunday's game, New Orleans had 8-1 odds at Caesars.
Bridgewater finished the game for Brees, going 17-of-30 for 165 yards in a 27-9 loss to the Rams. It was only the third time under Payton, who took over in 2006, that the Saints failed to score a touchdown.
Brees, 40, has missed only one start because of injury since high school -- when he was ruled out of a Week 3 game against the Carolina Panthers in 2015 with a shoulder injury.
Brees' absence will end his streak of starting at least 15 games in 15 straight seasons -- the second-longest of its kind behind only Brett Favre, according to ESPN Stats & Information.
Brees said it was tough for him to watch from the sideline Sunday. When he missed that game in 2015 at Carolina, he actually stood on the sideline and mimicked breaking the huddle before each play.
"It's very difficult not to be playing," Brees said. "I'm not used to that. I don't want to get used to that."
The Saints have invested heavily in Bridgewater, the former first-round draft pick of the Minnesota Vikings. They initially traded a third-round pick to acquire him last summer from the New York Jets.
Dual-threat quarterback Taysom Hill is another option for the Saints while Brees is sidelined.
Payton showed his support for Bridgewater after the game, calling him a "pro" who was ready to take over after Brees was hurt while blaming a lot of Bridgewater's struggles on the Saints' offensive line getting "whupped" up front and a slew of drive-killing penalties.
"I felt comfortable with Teddy and do feel comfortable with Teddy," Payton said.
ESPN's Mike Triplett contributed to this report.