The US international is said to be interesting the London club, though it is thought that Roma are only willing to let the 26-year-old go should they sign a replacement.
Bradley, who is the son of ex-US and Egypt international boss Bob Bradley, has already played for sides in Holland, Germany and even England, where he had a short loan spell at Aston Villa three years ago.
The combative midfielder was a key member of Roma's side last season, making 24 starts in Serie A.
However, a new coach in Rudi Garcia and the signing of Kevin Strootman in the summer have seen him fall out of favour, having made only six appearances so far this season.
Cardiff City were also thought to be interested, though the recent sacking of Malky Mackay could see their interest end.