The pair would become the fourth and fifth underclassmen to leave the program since the NCAA turned down a waiver request that would have allowed UConn to play in the 2013 NCAA tournament despite failing to meet academic qualifications.
Sophomore Jeremy Lamb and freshman center Andre Drummond announced earlier this month that they will enter this year's NBA draft, a move both were expected to make even if UConn had been eligible for the tournament.
Alex Oriakhi earlier announced he is transferring to Missouri for his senior season.
Coach Jim Calhoun told ESPN.com's Andy Katz on Saturday he remains optimistic the Huskies will have a winning season in 2013 and be a team that will challenge for an upper-division finish in the Big East despite the departures.
Smith, a 6-foot-8 forward, averaged 4.4 points and 3.4 rebounds in 33 games during his sophomore season, down from 5.4 points and five rebounds as a freshman, when he helped Connecticut to its third national title.
Bradley, a 6-10 redshirt freshman, was injured in the preseason and has never played a game for the Huskies. He was expected to compete for a starting job next season after the departure of Oriakhi and Drummond.
Bradley has expressed a desire to be closer to his home in Tennessee and his ailing grandmother, but Calhoun told Katz on Saturday that he was hopeful Bradley could still choose to stay.
If both Smith and Bradley leave, Connecticut would be left with just six returning scholarship players: guards Shabazz Napier and Ryan Boatright; swingmen DeAndre Daniels and Niels Giffey, and centers Tyler Olander and Enosch Wolf.
UConn has just one signed recruit, 6-foot-4 guard Omar Calhoun from New York. The school also has a verbal commitment from R.J. Evans, another 6-foot-4 guard, who plans to transfer from Holy Cross, where he averaged 11.5 points last season. Evans, who graduates this spring, has one more year of eligibility and could play immediately.
UConn is expected to try and sign at least two more players this spring.
The Huskies have not had a losing season since Calhoun's first as the school's head coach in 1986-87.
UConn faces a postseason ban because of several years of low scores on the NCAA's Academic Progress Rate.
In its waiver request, the school argued the penalty was applied retroactively and hurts current students, who had nothing to do with the low scores and have made significant improvements in recent years.
The NCAA's Committee on Academic Performance is meeting this week and may discuss changes to the APR that would allow it to use data from the two most recent academic years when determining a school's eligibility.
The governing body currently uses data from 2009-10 and 2010-11 in determining eligibility for the 2013 tournament.
UConn would qualify for next year's tournament under the proposed rule changes.
Information from The Associated Press contributed to this report.