It isn’t hard to pick out the moment Alexis Sánchez began to say his long goodbye. Last season’s Champions League last-16 tie against Bayern Munich is still a tender spot for Arsenal fans, one of those episodes of Total Collapse that have marked out springtime in the late Wenger years.

With 11 minutes gone in Bavaria Arsenal were 1-0 down, the defence apparently astonished to find Arjen Robben has a thing for dipping his shoulder, cutting inside and shooting. By the final whistle it was 5-1 to Bayern. But it could have been seven, or eight, or 12. In between times, as his team-mates curdled and turned green, Sánchez went nuts.

This is probably not the technical term, but then there was nothing that technical about an extraordinary display of pure footballing rage as Sánchez entered his own red zone, snarling, baring his teeth and entirely out on his own – a place from which he has only intermittently returned.

Sympathy for Alexis Sánchez. This a pretty niche position right now. The contract-refusal, the grasping agent, the obsession with his own elite destiny: the perception is this has all been a part of the Sánchez preservation society, repositioning himself to wring the largest possible final-contract payday from the Premier League’s endlessly gushing teat.

Currently this seems likely to lead Sánchez to Manchester United, who may be willing pay around £270,000 a week for his services, elite-level remuneration for an ageing individualist with one career league title to his name.

There is a natural note of weary cynicism about this. Take one mega-club in a state of retrenchment. Add one semi-megastar with a hungry agent, whose club career is in danger of unspooling into well-remunerated underachievement. Chuck in one trophy-crazed Portuguese short-termist. Welcome to modern football squared. The noodle partners will be delighted.

Except, like all ideas born out of football’s more cartoonish oppositions, this is only half the story. In reality Sánchez to United could end up an excellent move for all concerned.

Over the full three and a half years that contract would add up to £50m and as a total package around £100m, or the equivalent of a more standard (insanely inflated) wage plus a £75m transfer fee. This is pretty much what United would pay on the open market.

Meanwhile Sánchez will obviously improve the team. United have a two-tier squad at the moment, with a large helping of talented young players and ageing stalwarts.

There is a vacancy for a ready-made prime-career star, already Premier League-trained, able to walk into the team and simply give it another edge, another way to win. Probably Sánchez, 29, would end up playing behind the centre-forward at United, or up front himself. But it isn’t hard to see him driving the way United attack for the next two seasons.

José Mourinho could do with a galvanising spirit such as Alexis Sánchez in his Manchester United team. Photograph: Matthew Peters/Man Utd via Getty Images

Plus of course there is the José meets Alexis angle, a manager with a desperation to win that verges on the poisonous, and a player who seems to have been running his own three-season self-destruction rule at Arsenal. The Special One meets the Small Angry Scuttling One: mix and stand well back.

Except, again it’s not quite this simple. The notion of Sánchez as a malcontent superstar is unfair. In many ways his reaction to being an Arsenal player is entirely reasonable. Maybe, just maybe, he’s frustrated because Arsenal are frustrating. Perhaps he’s disillusioned with being at the Emirates because being at the Emirates is disillusioning.

Mesut Özil also played in Munich last year but he didn’t descend into a state of wild, snarling fury. Instead he made 20 passes over the full 90 minutes and walked off at the end an elegant ghost.

Little wonder, perhaps, Alexis got cross. But he is also a warrior, a relentlessly effective footballer who isn’t worried about being nice, sulks, digs his nails in, is utterly desperate to win. Wait. Who does that sound like?

And really it is that as-yet rather overlooked meeting of sporting souls with José Mourinho that is the most intriguing part of Sánchez to United – and for more productive reasons than simply a shared toxicity. There have been players during each of Mourinho’s successful club spells who have seemed to reflect and amplify his own dark lust for glory, his galvanising spirit.

Right now Mourinho could do with another one of these. He is wrestling with the wheel of a juggernaut, on his way to a sixth season with just the single league title, eight years since his last Champions League, desperate to reburnish his image as a serial elite winner.

Similarly, for all his qualities Sánchez has never won anything of any real consequence in club football. He still has the opportunity. It could be a fascinating moment of intersection, with all options still open: drift, meltdown, muddle; or, just as likely, a little late-breaking shared sporting redemption.