Bristol City have held a long-term interest in Smith after the former Oldham Athletic and Leeds United striker enjoyed a successful spell on loan at Ashton Gate last season.
The powerful forward scored 13 goals in 20 appearances for Bristol City last season and he quickly established himself as a big fan favourite with the club faithful.
City were keen to make his move permanent in the summer, but Fulham decided to snub their overtures and keep Smith at Craven Cottage.
The 26-year-old has struggled for regular action at Fulham this season with Ross McCormack and Moussa Dembele ahead of him in the pecking order.
Smith has just started four games in the Championship this term and has netted only one goal in 15 appearances.
Bristol City are keen to bring Smith back to Ashton Gate as they see him as someone who can score the goals to fire them to safety in the Championship.
However, Fulham have rejected a substantial bid for Smith as they are reluctant to lose the forward with the club currently under a transfer embargo and doubts regarding the futures of both McCormack and Dembele.