In relief in 2015, Osuna converted 20 of 23 save opportunities while notching a 2.58 ERA.
However, Osuna has experience starting in both the Mexican League and the Minor Leagues.
One challenge would be to figure out how many innings Osuna could log as a starter. The 20-year-old has never pitched 100 innings in a season.
"He's a different kind of guy," LaCava said. "He's pretty unique. I don't put any limits on him personally, but obviously we would get with all our people and discuss that and see what's best for everyone involved. We'd have to put our heads together and decide on a good plan that was good for him and for us. That would be to be determined."
Liam Hendriks and Aaron Sanchez are two other relievers the Blue Jays could convert to the rotation, depending on how the offseason goes.
"We're open to all things," said LaCava. "We haven't made any final decisions on any of those guys on whether we're going to lengthen them out or not. All three have the possibility to do that, and we'll just look into that as we get further into the offseason."
The Blue Jays hope that righty starter Drew Hutchison, who had a 5.57 ERA in 2015, can be nearer to the pitcher he was in '14, when he had a 4.48 ERA in his first full season in the big leagues.
"Drew's a great competitor, as you've seen," LaCava said. "There's nobody that wants to be good more than he does. If you look beyond some of the stats and look at some of the underlying things, he still shows signs of being the pitcher we all know he can be. We're really hopeful that this [next season] he comes out and takes that step, and we believe he will."
Right now, LaCava envisions Hutchison being one of the club's five starters in '16.
If Marco Estrada accepts his qualifying offer by Friday's deadline, that would be a significant event for the Blue Jays. The righty was 13-8 with a 3.13 ERA in 2015, starting in 28 of his 33 appearances.
"Friday's deadline is coming up, and we obviously want to secure Marco again," said LaCava. "We'll see how it works."