Piatek has been in deadly form this season, scoring 13 goals in eight games in all competitions, including nine in Serie A.
That tally makes the Poland international the top goalscorer in the Italian top-flight, having scored three more than Napoli's Lorenzo Insigne, four more than Lazio's Ciro Immobile and five more than Juventus superstar Cristiano Ronaldo.
His goalscoring exploits have led to reports that Chelsea could make a bid worth £60 million (€68m/$78m) for the 23-year-old, who joined the club from Polish top-flight side Cracovia.
Tomasz Magdziarz, his agent, says his success has come about as a result of his down-to-earth personality, but he maintains there is yet to be any formal interest in his services.
Asked by Goal why he has hit the ground running, he said: "I think because he is a very modest person. He has had a big impact in Serie A but he stays himself to everyone.
"We are in contact with a few clubs but we never give any information about it to the press."
However, Magdziarz also says Piatek, who has already been compared to Bayern Munich striker Robert Lewandowski, is not closing the door on a move to the Premier League.
"Serie A is his home at this moment but we dont know what future will bring," he added.
Genoa's chairman, Enrico Preziosi, has also confirmed that clubs are interested in signing Piatek, and he is expecting the striker to eventually leave his side.
"We are already full of phone calls for him, I'm sure that [a top club] will take him away from us," he told Gazzetta dello Sport.
"I will decide the price, but a lot of Italian and top European clubs are interested in our player."