A photo of the Giants' logo appeared on his social-network account with the caption: "My soon to be new home".
Hashtags including #moneyoverloyalty, #byealistair and #upthegiants were also used.
The photo attracted more than 1400 likes before it was deleted.
Stride Management later issued a statement on his behalf confirming Franklin's Instagram account had been hacked.
"This is an extremely disappointing situation and we will be investigating how this occurred and working to ensure this type of thing doesn't happen in the future," Franklin's manager Liam Pickering said.
"In the meantime please do not take any notice of what is posted until this is rectified.
Franklin last week said he would not make a decision on his AFL future until after the season with the Giants reportedly tabling a $10 million offer for his services, while the Hawks reportedly also made the biggest offer to the forward in the club's history.
