I'm not aware that Franklin ever expressed any interest. Though he may have had some interest. His last term as President of Pennsylvania ended roughly a month before the first presidential election. So he was still active in politics.

That said there were 12 men who received electoral votes in that first election, and Franklin wasn't among them. Had he been interested in the job, he likely could have garnered enough support to make a decent run at Vice President. Washington had the Presidential job sewn up long before the election. But by that point he was well into his 80s. He would die just a little more than a year later. And there are stories about how he didn't do much in either of his last two governmental positions (representative at the Constitutional Convention and President of Pennsylvania). His health was evidently preventing him from being really active in either position.

So I would say, interest or not, his window had closed. His advanced age and declining health probably precluded any run.