Suarez cost Liverpool £22m from Ajax in January 2011 but has had a mixed first year in England.
He has scored 16 goals in 45 games for the reds, but was also banned for eight games for racially abusing Manchester United defender Patrice Evra.
Liverpool have suffered a run of six defeats in seven games, which is their worst spell for nearly 60 years.
According to Corriere Dello Sport, Roma and Juventus have both been in contact with Liverpool about a summer transfer and are lining up bids of around £25m for the 25-year-old
Source: DSG