Ipswich Town's Smith
Smith's contract was thought to have expired last month, however, he appears to have remained a Town player, and Fulham are willing to pay £750,000 for his services, the report claims.
The Cottagers have offloaded centre-backs Dan Burn and Shaun Hutchinson this summer, potentially creating space for the New Zealand international.
However, Reading have recently allowed Anton Ferdinand to leave, while Blackburn pair Grant Hanley and Shane Duffy are said to be courting interest from elsewhere, leaving both clubs in need in Smith's position.
Hanley is reportedly wanted by Newcastle United and Sheffield Wednesday
The 26-year-old has been a regular for Town since making his debut at the end of the previous decade and has made over 250 appearances.
Mick McCarthy's side have already added Portsmouth centre-back Adam Webster to their ranks this summer and could welcome an approach for Smith as they look to raise funds for further deals.
Defender Webster has already signed up at Portman Road
Macclesfield-born Smith is predominantly left footed and can also provide full-back cover if required.
Smith in action last term