Shanahan is interested in the job but is currently focused on Sunday's NFC Championship Game. The Falcons will host the Green Bay Packers.
The 49ers plan to request a second interview with Shanahan next week after the championship game, a source said. NFL rules allow a second interview following the conference championship.
New England Patriots offensive coordinator Josh McDaniels took himself out of the running on Monday, saying it wasn't the right time and he was going to concentrate on New England's Super Bowl run.
Seattle Seahawks assistant head coach/offensive line coach Tom Cable was also among the candidates considered by the 49ers, but his agent, Doug Hendrickson, tweeted Tuesday that Cable is "re-affirming'' his commitment to the Seahawks and thanked the 49ers for their interest.
Just spoke with my client Tom Cable and he is reaffirming his commitment to the Seahawks. He wishes to thank the 49ers for the consideration— Doug Hendrickson (@DHendrickson41) January 17, 2017
Shanahan, 37, is in his second season as Atlanta's offensive coordinator. The Falcons, led by MVP candidate Matt Ryan, boasted the league's top scoring offense this season, averaging 33.8 points per game.
Besides interviewing with the 49ers, he also talked to the Broncos and Jaguars about their head-coaching vacancies before Denver hired Vance Joseph and Jacksonville promoted Doug Marrone to fill their jobs.
Before joining the Falcons, Shanahan was the offensive coordinator for the Cleveland Browns (2014), Washington Redskins (2010-13) and Houston Texans (2008-09). He began his NFL coaching career in 2004 as an offensive quality control coach for the Tampa Bay Buccaneers before joining the Texans in 2006 as a wide receivers coach. He was the team's quarterbacks coach in 2007 before being promoted to offensive coordinator the next season.
Shanahan is the son of longtime NFL coach Mike Shanahan, who hired his son as the Redskins' offensive coordinator when he was the team's head coach.
The 49ers are seeking to replace Chip Kelly, who was fired as coach after just one season. San Francisco, which finished 2-14 last season, holds the No. 2 pick in the 2017 draft.
The 49ers are also in need of a new general manager after firing Trent Baalke after the season.