As a manager and somebody who enjoys being able to pay my bills, wouldn’t mess with any of this. I have had subordinates take interest in developing a personal relationship with me. In some cases I share that feeling, but I still tell them as their manager it would not be appropriate to proceed due to the potential impact in the workplace. Quick way to get accused of giving special treatment and moved or terminated. Very hard to hide.
If you and Jane are in an equal level role or one of you is willing to quit or change roles, go for it.
John’s personal problems sound like they are effecting his work performance. If you are his supervisor you are responsible for handling that in some way. If you let too much slide because you feel bad for him, this will go from a problem with John to a problem with you. It is John’s responsibility to manage his personal life and be able to do his job within the expectations of the company. If you are sharing that the expectations aren’t be met in similar ways multiple times, cut the cord.
Regarding your expectation of John taking issue with you and Jane becoming a thing, kinda depends what Jane wants if you ask me. And I’m sure it’s scary how John would react being rejected but again, that’s on John to deal with. I’d just be straight up about it. Sorry man she’s into me and I’m Into her. That’s bad news, but if he can’t handle that in a mature manner that’s on him. He’ll end up quitting or getting terminated for an emotional outburst. It’s sad, but it isn’t your responsibility to control how he responds. Personal problems are personal problems. Generally, managers that are managing lower level managers understand when somebody on the team just doesn’t click or behaves in a way that wasn’t within your control or purview. They have been through the same shit themselves.
Ensure you are operating within the confines of your handbook/guidelines if you want to keep your job. That’s the biggest thing.
Expect this to become an HR issue if John doesn’t immediately quit. I would avoid moving forward with an attempt to terminate John after he identifies the you and Jane situation as that may look retaliatory. Either get HR or another manager involved to ensure John is clearly being terminated for valid reasons and that other people are involved in that decision.
If you want to go the more sinister route (some people do). Terminate John with solid documentation on the performance issues. Negative attitude possibly. Consult your handbook for options, but ultimately you can terminate him and wait on moving forward with Jane until he’s gone.
If you take nothing else from this, consult the handbook. If you want to keep your job all the information is in there. You can get it from HR in the event you don’t already have a copy.
This is a horse to water thing. You don’t have control of the outcome, you can only provide John the tools to keep his job. Most managers have a list of folks they tried their best with, but it didn’t work out. I look back on those folks with a great deal of sadness, but it’s about the team. If you told him how to benefit the team and he chooses not to that it’s on him.