There's still some time before training camp kicks off, and things could turn around if he gets the all-clear, but it's starting to look less likely that he'll be joining the Leafs. The recent news that he never actually signed a contract points to his health being the real issue here, with nothing moving forward until he's fully cleared by all of the doctors involved.
When Jani Hakanpaa was first rumored to be joining the Leafs, word got out that he was dealing with a «degenerative knee» problem, which is why the Stars let him walk in free agency. Toronto's medical staff initially gave the thumbs up to GM Brad Treliving to pursue him, but it seems they might have found the same knee issue now, which has led to this ongoing contract stalemate.
With training camp right around the corner and preseason not far off, they'll need to sort this out quickly. Whether the NHL will process Jani Hakanpaa's contract remains to be seen, but it's not looking too promising right now. If the deal falls through, the Leafs will need to switch gears fast in order to find another right-handed defenseman in free agency. On top of all this, they still need to figure out what they're going to do with restricted free agent Nick Robertson, and they are likely waiting for the Hakanpaa situation to get resolved first before they move on to anything further.