After carefully going over the team needs of the Leafs, and the market of availability, I have compiled the following list of players that the Leafs might be able to get in order of preference. I have also put the needs to trading partners as well.
Calgary - Brodie (UFA)
New Jersey - Subban - Futures (50% retained)
Columbus - Savard (1 year til U) - Offense
Edmonton - Larsson (1 year til U) - Offense
Vancouver - Tanev (U) - Injury Prone
Calgary - Hamonic (U)
All of these players are RD except for Brodie, who is capable of playing RD. Subban is a bit of pipe dream, and I'm not sure he should be a target given what he will likely cost, but he's there anyway. These defensemen all play about the same regardless of the minutes they play. Also, Brodie and Tanev are the only ones on the list who did not have a down year. They will likely be in the most demand.
You may notice that there are players missing from this list that have been mentioned in several posts. Alex Peitrangelo will not be signed by Toronto. He will demand 9 million roughly. The Leafs would have to move out one of the big 4 to get him, or Morgan Reilly. They would need to take back futures only. I can't see that happening. Aaron Ekblad is too important to Florida to move. Matt Dumba is an achievable trade target, for one of the big four. I think the Leafs have considered this and have determined that he is a step back from each of the big 4. Still, Minnesota would want nothing less. Gudas plays worse the more minutes he plays, like Polak (and Dumba tbh).