Having already swooped for Ashley Cole, Roma may add another Englishman to their defensive line ahead of next season.
The Giallorossi are trying to strengthen in preparation for a title challenge, having finished as runners-up last season to Juventus.
Much of Roma's transfer policy has been dictated by attempts to keep hold of defensive star Mehdi Benatia and the Moroccan centre-back's future remains uncertain.
At the moment Roma are attempting to persuade Benatia to stay put and sign a contract extension in the face of alleged interest from Bayern Munich.
The paper believes that Roma are looking at Tottenham defender Vlad Chiriches and Lille defender Marko Basa, but they may also consider Richards.
Richards was said to be on Roma's radar ahead of last January's transfer window and he may be on his way out at Manchester City.
The 26-year-old's career has stalled badly of late and his contract expires next summer, so it is suggested that Roma may be able to land him for just £4 million.
However, recent reports in England have claimed that City are demanding at least £7 million for Richards, which has been putting off potential interested parties.