Gilardino said, however, that he would not be thinking about his future until after he returns for Genoa's pre-season.
"Roma? Each time your name is linked to big sides it's a pleasure," Sky Sports News quotes Gilardino as saying. "However, now I'll have holidays and we will see what will happen."
Gilardino joined Genoa in 2012 from Fiorentina but spent most of last season on loan at Bologna.