Speaking on AFL.com.au's Gillette Trade Radio, Bond said the Dockers were acutely aware they had to address their lack of quality talls, and both players were firmly in their sights.
Bond said Fremantle had not ruled out trading for both key forwards.
He said Sydney Swan Jesse White was off the radar though, after White indicated a desire to be traded to Collingwood.
Although in the early stages of considering a chase for Geelong premiership player Podsiadly, Bond said they had made contact with his management and the signs were positive.
"The feedback we're getting is James is really keen to continue his career and really keen to strive to get another premiership under his belt, and hopefully we're a club he can see that in," Bond said.
"The feedback has just been glowing on him. As a person, the way he handles himself and it's a great story, he waited 10 years to play his first game."
Bond said chasing a player of Podsiadly's age (32) was not the usual Dockers model, but said without developing their own key talls in recent years, they had to look to the trade table.
Captain Matthew Pavlich and star fullback Luke McPharlin both turn 32 in December and need help.
"Once you start talking somebody of that age and experience to come through your door, they need to offer more than talent, and James does that," Bond said.
"People who know him, know the quality of person he is."
Fremantle chased Essendon's Gumbleton last year and are again after him this year.
The 25-year-old West Australian has played just 32 games in seven injury-plagued seasons for the Bombers, and Bond said the Dockers would contact his manager Paul Connors shortly.
"We all know his story, a high draft pick a number of years ago (no.2 in 2006) and it's been quite tragic what's happened to him. His resilience has been outstanding to fight his way back," Bond said.
"We'll continue with our due diligence and we already know from last year he's a quality person as well."
"Either of those two (Podsiadly or Gumbleton), if it was to eventuate, has to be desperate to play, and keep doing everything they can to improve our club."
Despite the rumours, Bond said Fremantle never entertained trading midfielder Nat Fyfe to Greater Western Sydney for the first pick in the national draft, and never even asked the question.
He said Fremantle would continue to assist 20-year-old Josh Mellington in trying to get a trade back to a Victorian club as he has requested.
