Former Blues president Stephen Kernahan admitted in March he would like his premiership teammate to rejoin the club.
"I am currently contracted to the Giants. After a successful trade period, the club is now focused on next month's NAB AFL Draft and contract extensions for a number of our players," Silvagni said.
"We hold a strong position at the draft and look forward to continuing to build on the gains made last week with the recruitment of Ryan Griffen and Joel Patfull."