Sunderland counterpart Steve Bruce and Celtic's Neil Lennon have already raised the possibility of recruiting the Welshman and Hughes has now joined them.
If Bellamy did move to Craven Cottage it would be the third time Hughes had signed the 31-year-old after also taking him to Blackburn and City, while he played with and under the Fulham boss when he was in charge of Wales.
Bellamy appears surplus to requirements at Eastlands and has been left out of City's squad for their Europa League qualifier against Timisoara despite there being room for two more players in the pool.
Source: PA
Source: PA