I'm afraid I'm not sure about this view that Mancini's history with us would prevent him from being interested in the United job. Yes, I think he formed a genuine attachment for our club when he was here. However, he's steeped in Italian football and seems to have attitudes that are fairly common in that country.
One of those is that players and managers appear much more willing to serve the bitter rivals of clubs they've previously represented. I think he'd go to United if he really felt it were a desirable career move.
I still doubt it'll happen. For one, it relies on Italy not qualifying for the World Cup in November/December 2022, as he won't walk out beforehand if they're going to take part. They do have a tough play-off final and will have to win in either Lisbon or Istanbul to get through, so it's not a given, but they're the best side of the three in question and may well make it count.
Second, the sainted Ralf could easily do well enough either to continue in the manager's job or to have a significant upstairs role at United. If the latter, he'd be far too interventionist for him and Roberto to rub along easily.
Still, IMO Mancini is likely to decide on the prospect with the kind of dispassionate attitude most of us have when deciding whether to take a new job. I wouldn't personally blame him for that or regard it as tarnishing his legacy with us.