Roma are looking to strengthen their attack in January and have previously been linked with Spurs striker Roman Pavlyuchenko and Bayern Munich star Luca Toni.
Il Corriere dello Sport says Roma could make a move for Zigic, who has recently returned to Valencia from a successful loan spell at Racing Santander.
“I want to leave because I want to play. I am ready to leave on the condition that I find a better team than Valencia,” he said.
Roma would prefer taking the 29-year-old on loan until the end of the season with a view to a permanent deal in the summer.