The 31-year-old hot-shot has been linked to Premier League sides West Ham and Sunderland, as well as Italian Serie A outfits Bologna and Sassuolo.
But Gilardino - who ranks among the top 15 all-time scorers in Serie A - wants to stay at his present club as he seeks to notch 200 goals in the Italian top division.
He would also try to earn his place in this summer's Italian World Cup finals squad, having being part of the 2006 winning squad and also being selected in 2010.
Gilardino told the club's official website: "There have been many rumours but I want to stay at Genoa, I am fine here.
"Attracting interest from other teams always gives pleasure, it means that your qualities are appreciated.
"My goals? I'd like to get to 200 goals in Serie A and take part in my third World Cup, but now I think about the present and to do well with Genoa."