Smart's Rams lost to Indiana on Saturday, ending their season in the round of 32. VCU became just the third No. 11 seed in NCAA tournament history to make it to the Final Four in 2011, after which Smart signed an eight-year extension.
The Illini did not make the NCAA tournament this season, and it cost Weber his job.
The 34-year-old Smart is considered one of the brightest young coaches in the nation, and his hiring would end Illinois' distinction as having never hired a minority head coach in football or men's basketball.
Illinois athletic director Mike Thomas appeared on "Chicago's Gamenight" on ESPN 1000 on the day Weber was fired and praised Smart's abilities. Smart worked as an assistant coach at Akron when Thomas was the Zips' AD.
"Shaka, you can see what he's done at VCU, obviously done a bang-up job," Thomas said on March 9. "He's a sharp guy. He's someone that has a strong background. He's done great things at VCU ... I think we'll have great interest in this job. I don't think there's any doubt it's a high-profile job. And in my mind probably one of the top 15 or 20 jobs in the country."
Thomas said he will consider diversity in making this hire.
"For me as it falls under my job description, it's really about hiring the best basketball coach," Thomas said. "But in saying that, it's also my job to make sure we have a quality pool and a diversified pool. We gotta have some diversity. It's gotta be a pool of strong candidates. But at the end of the day, it's my job to get the best basketball coach for the University of Illinois."
Smart is a Wisconsin native, and his wife Maya is a Northwestern alum.