Franklin has put contract negotiations with Hawthorn on hold until the end of the season, sparking rumours that he is keen to test his value on the open market.
Fremantle have been heavily linked to the 26-year-old, while West Coast are another club rumoured to be in the frame, given Franklin's WA heritage and the fact he used to share a house with Eagle Sharrod Wellingham.
Lyon admitted Fremantle was in the hunt for Collingwood's Travis Cloke last year, but he said Franklin wasn't on the club's agenda.
"I went to a Coaches' Association sub-committee meeting, and Alastair Clarkson was there," Lyon said on Wednesday.
"I sought out Alastair, and I said to him, 'This is not us - just to let you know so you don't have to worry. It is not us'.
"That's on the public record, and that hasn't changed.
"I can't be any clearer than that."
Lyon said his priority was to re-sign his current list, and said clubs like Greater Western Sydney and Gold Coast were far better placed to accommodate an expensive signing like Franklin.
