The 31-year-old, who has scored eight goals in 19 appearances for the Grifone, has said that he wants to make Italy's World Cup squad by playing for Gian Piero Gasperini's side rather than moving to West Ham United.
"While the coach and the president (Enrico Preziosi) have always know this, I work at my maximum to give everything for the shirt of Genoa," he told SportMediaset.
"If I were to go to Brazil, then it would crown my career in an extraordinary way. The next few weeks could change our season. Our goal, however, remains league survival.
"From now until May, it will depend on what I can do with Genoa, for my performances and goals. Personal goals? In Serie A I hope to reach the 200-mark in goals and surpass that, as Francesco Totti did."
Genoa are currently 10th in Serie A.