The team allegedly reached out to the 44-year-old player after Sam Bradford, the Rams' quarterback, suffered a season-ending ACL tear on Sunday. If the conversation did indeed take place, the NFL legend turned down the offer.
The Rams ended up signing Brady Quinn and Austin Davis for the job, but according to ESPN's Adam Schefter, Favre was the team's first choice.
"It's flattering, but you know there's no way I'm going to that," Favre said of the Rams offer during a radio interview on Thursday.
He added that his last season with the Minnesota Vikings, in 2010, had convinced him that it was time to stop playing after a shoulder injury ended his consecutive starts streak at 297.
"I had a great career. I think if anything, the last year that I played was an obvious writing on the wall, vision for you if you will," he said. "It was time."
Favre added that he is happy with his life away from the game that made him famous and that he is ready to put his family in the front seat of his life.
"I've taken trips that I never thought I'd take, I've gone to Yellowstone and I've gone Glacier National Park, I've gone to steamboats, my snow skiing, we've gone down to the Bahamas, we've done things that really everybody in my family just kind of waited for."
Additionally, he said his body is in no condition to endure another season at the NFL.
"I'm like a yardstick, I'm so stiff," he added. "So I'm just trying to ... not stay in shape to play, but stay in shape to do everyday things, not only with my daughter and my wife and my grandson, but really just for me."
2014: The Year in Music [PHOTOS]