The Giants have had discussions with Franklin's manager, Liam Pickering, with a $10 million package over six years reportedly on the table, although not yet the subject of an official offer.
With that sort of offer the Giants would almost certainly be able to acquire Franklin as a restricted free agent in October's free agency period, with the Hawks highly unlikely to match it.
Asked on Thursday whether the Giants would use the No. 1 pick they currently hold to trade for Franklin, Giants list manager Stephen Silvagni said "anything's possible".
"It might be free agency if he does decide to become that free agent or it might be a trade situation," Silvagni said of the Giants' means of securing Franklin.
"We just don't know. I guess it's still too early in the season to give you the right answer."
Although the Giants' talks with Pickering remain ongoing, Silvagni said GWS was unlikely to speak with Franklin before he decided his football future.
"We're talking to his management group but having said that he hasn't made a decision and he doesn't want to talk to us in terms of making a decision," Silvagni said at a Giants boardroom lunch.
"That's where that sits at the moment."
Silvagni said it would take "a super, super" deal for the Giants to part with the No.1 pick, but confirmed he had already had preliminary trade discussions with "a couple of clubs".
Clubs looking for a key forward will presumably be desperate to get their hands on the first draft pick, with Eastern Ranges spearhead Tom Boyd widely considered the best player in this year's talent pool.
Silvagni suggested those clubs would need to offer the Giants strong-bodied players with at least four years AFL experience who could support their core of elite youngsters.
Regardless of what Franklin decides, Silvagni said the Giants would be "very active" in this October's free agency and trade periods.
"We need to get stronger bodies," Silvagni said.
"Generally it takes a player four to five years to become a bona fide senior player in terms of body size. A lot of our boys are only in their second year of footy so we understand we've got to get some strength whether that's in the midfield, up forward, down back.
"We've got to get some senior bodies through the door and that's what we'll be doing."
Nick Bowen is a reporter with AFL Media. Follow him on Twitter @AFL_Nick
