Giovinco has only recently been linked with a return to Juventus, who still own 50% of the player's rights, after the club were said to have earmarked him as a long-term replacement for Alessandro Del Piero, who is expected to leave at the end of this season.
However, it now appears Juventus will face a fight for his services, if D'Amico's claims are proven to be true.
"It's no mystery that [Chelsea owner] Roman Abramovich likes Giovinco," D'Amico said, according to Sportal.it.
"The Chelsea owner was struck by Giovinco's performances when he played against them for Juventus [during the 2008/09 Champions League campaign]."
Furthermore, D'Amico claims Chelsea manager Andre Villas-Boas is also a fan of the dimunitive playmaker.
"Also, Chelsea manager Andre Villas-Boas loves the player's technical qualities, and this means he is someone who understands [football]."
Nonetheless, the agent was quick to insist no contact had been made by Chelsea, and that much would depend on Parma's willingness to allow their prized asset to leave the Stadio Tardini.
"Chelsea would be a nice club [for Giovinco to join], but at the moment there is nothing concrete.
"It all depends on Parma - they will decide. Plus, we would have to wait for an offer."
Giovinco has started the season in stunning form, and has already six goals in seven games for Parma in the Serie A.