The USA international has attracted the attention of several clubs, including the Giallorossi, after an impressive first season in Serie A.
"Michael is excited about Roma's interest," Bradley's agent Alberto Faccini said to www.calciomercato.com. "It's always nice for a player to be linked with a renowned club as Roma."
The 24-year-old, who joined Chievo last summer from Borussia Monchengladbach and made 31 league appearances for the Verona outfit, has also been strongly linked with a move to Fiorentina.
"Fiorentina expressed an interest in the player and when I spoke to Michael he was flattered," Faccini said. "We have never rejected Fiorentina.
"Roma are very interested in the player, but (Roma sporting director) Walter Sabatini and Chievo will have to agree something."
Bradley has one year left in his contract with Chievo.