Trent Baalke, 49ers general manager, said last week that the topic of trading Smith to an NFC West team was not discussed when he had dinner with Smith and his wife, Elizabeth, shortly after the Super Bowl.
The Cardinals are interested in Smith because of his "experience, intelligence and talents," the source said. Smith had his best season in nine starts in 2012, as he completed 70.2 percent of his passes with 13 touchdowns and five interceptions for a passer rating of 104.1.
The Cardinals have plenty of uncertainty at quarterback. The club acquired Kevin Kolb from the Philadelphia Eagles in the summer of 2011. Kolb earned $20 million over the past two seasons. He is due a $2 million roster bonus on March 17, and his scheduled salary is $9 million.
Kolb, John Skelton, Ryan Lindley and Brian Hoyer started games for the Cardinals, who finished with a 5-11 record after winning their first four games. The Cardinals fired coach Ken Whisenhunt and hired former Indianapolis Colts offensive coordinator Bruce Arians in January.
Smith is scheduled to make $8.5 million in 2013. He is signed through the 2014 season.
The Kansas City Chiefs are also expected to be interested in working a trade for Smith. No trade can be completed until March 12 at 1 p.m. (PT), when the new league year begins.