The 39-year-old outfielder did not play last season but never retired. La Russa said Edmonds began texting him about a comeback the day before Sunday's Animal Rescue Foundation event in St. Louis, and at first the manager thought it was a joke.
La Russa said he got more texts from Edmonds during the event asking if he could come on stage, where he asked for another shot.
"I thought he was going to just say how much he enjoyed the show," La Russa said Monday. "He's serious. I said, 'If you're serious, we'll give you a serious discussion out of respect.'
"Beyond that, I don't know."
The starting outfield is set with Matt Holliday in left, Colby Rasmus in center and Ryan Ludwick in right. But the team lacks depth heading into spring training and Edmonds, who played for the Cardinals from 2000-07, could be a fit as a fourth outfielder.
Edmonds batted .235 with 20 homers and 55 RBIs in 2008 with the Cubs and Padres. He was a big part of 100-win teams in St. Louis in consecutive seasons in 2004-05, and played on a World Series winner in 2006.
The Cardinals traded Edmonds and $2 million of his 2008 salary in December 2007 for prospect David Freese, the leading contender for the vacant third base job in St. Louis.
"That would be great having him back, but I don't make those decisions," Albert Pujols said of Edmonds. "If he's in good spirits to come back and in good shape, I think we definitely can use his help in our lineup."
La Russa dismissed the notion it might be difficult to cut Edmonds if the comeback fizzled.
"If you do your job right, your honesty with players is one of the key things," the manager said. "If he wants an opportunity here or anybody wants an opportunity here and I can't feel like I can tell him he's not good enough, I'm the wrong guy for the job.
"With Jim, I have no problem telling the truth."