The earliest San Francisco can complete a trade of Smith is on March 12 after 4 p.m. ET, which is when the 2013 league year officially begins.
There is no deal in place right now, sources said.
Smith, the 2005 No. 1 overall draft pick, lost his starting job to Colin Kaepernick in November while sitting out with a concussion but was professional at every turn and continued to mentor his replacement.
Before his injury, Smith had completed 26 of his last 28 passes -- including going 18-of-19 for 232 yards, three touchdowns and no interceptions in a "Monday Night Football" win at Arizona on Oct. 29.
He then sustained a concussion in the second quarter of the 49ers' next game, a 24-24 tie against St. Louis on Nov. 11. Smith sat out the next game as Kaepernick dazzled in his debut as an NFL starter, beating the Bears handily at home on "Monday Night Football."
Smith didn't start again last season but was credited by coach Jim Harbaugh in the week before the Super Bowl for mentoring Kaepernick despite losing his starting job.
The 28-year-old quarterback has thrown for 14,280 yards with 81 touchdowns and 63 interceptions in 80 career games.
Information from The Associated Press was used in this report.