The Serie A outfit are set to swoop for the defensive midfielder after other options proved too expensive, while Corinthians defender Castan is an imminent arrival
The 24-year-old only joined Chievo from Borussia Monchengladbach in 2011, after an unsuccessful loan spell at Premier League side Aston Villa.
However, the American now looks likely to move again with the Giallorosso reportedly chasing the player alongside Palermo, Fiorentina and Juventus.
The club's sporting director, Walter Sabatini, had been rumoured to be interested in tempting Italian defender Federico Balzaretti away from Palermo, after his impressive displays with the Azzurri at Euro 2012.
However, it seems that the club's valuation of no less then €12 million is too high for Roma, and they are therefore looking to strengthen in other areas of the pitch by bidding for Bradley.
Roma are also on the verge of completing the signing of Corinthians defender Leandro Castan for €5 million, on a four-year-deal. The highly rated 25-year-old is set to join up with the squad in late July after a holiday.