Gordon said the club had not yet made a decision yet on whether to indulge the skipper's request, given he still has one year left on his contract.
The Giants have pick No.4 in this year's NAB AFL Draft, but will likely have to sweeten the deal with another pick or a player to win over the Bulldogs, with Gordon demanding a high price.
"We'll deal with it in the smartest and [most] strategic way that we can," Gordon told radio station Triple M.
"Let's look at Ryan Griffen, he's just played his 200th game, captain of the club, All-Australian, one of the most credentialled guys going around.
"There wouldn't be a player, except maybe Gary Ablett, that's changed clubs in the last couple of years that's had the cachet and the value that Ryan Griffen has got.
"Dealing with it on a theoretical level, if we agreed to that sort of request, then the sort of quid pro quo we'd be looking at would be pretty much unprecedented in the competition. "
If the Bulldogs bow to Griffen's request, he will join former teammate Callan Ward at the Giants, after he left the kennel at the end of season 2011.
The club also lost Jarrod Harbrow to Gold Coast at the end of 2010.
Gordon declared the Bulldogs were not "cannon fodder" for the AFL's newest clubs, and vowed the club would hit back.
"We're in this to win it," Gordon said.
"It's been a tough week at the office for us but you can expect us to fight back as aggressively, and as creatively and as strategically as our members are entitled."
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