When Alessio Romagnoli scored the penalty that sent Milan into the Coppa Italia final on Wednesday, cutting through the Stadio Olimpico chill to see off Lazio at last, the noise around the Rossoneri’s on-pitch revival hit its highest pitch yet. In the aftermath Rino Gattuso, architect of a 13-game unbeaten run, felt compelled to underline that he is “not a great coach … not a guru of the bench”; Leonardo Bonucci, meanwhile, was moved to hail achievements that “just a few months ago seemed impossible”. The inescapable sense was that of a tide turning at long last.

Arsenal will provide the next test of Milan’s new-found strength, with the first leg of their last-16 Europa League tie in Italy on Thursday, but the nagging fear – beneath the wave of comparisons between Gattuso and Antonio Conte, as well as the obvious relief that Bonucci’s costly summer move from Juventus is beginning to look worthwhile – is that a far more fundamental, and serious, weakness lies beneath.

The murmurs about their financial situation, the source of endless speculation since Li Yonghong’s takeover was finalised in April 2017, will not go away and unease will persist at the very least until Uefa, which is monitoring their adherence to financial fair play, makes any sanctions known in the coming months.

It was certainly an unusual way to see in Chinese New Year when Li, in a statement that began with compliments of the season, launched into an impassioned defence of his ownership, aimed “to calm down the environment around the club and the team”. That was on 20 February and followed an investigation from the Corriere Della Sera, whose headline read: “The safe that Milan bought was already empty.” The paper claimed Li, whose Rossoneri Sport Group purchased Milan for £628m, is essentially insolvent and that a court has arranged for his stake in a packaging company, Zhuhai Zhongfu, to be auctioned on Taobao, the Chinese equivalent of eBay, in order to repay two banks. It arrived at three possible conclusions – that Li is indeed highly wealthy but has hidden the source; that he is a “mythomaniac”; or that he is caught up in a game bigger than him – before reaching the most important: “That Milan does not end up on Taobao”.

Li’s statement was, considering the nature of the allegations, hardly illuminating. “I want to … take the opportunity to explain – hoping this will be the last time – that the situation concerning my assets is safe and sound and that both the club and my companies are steadily working,” he said.

There has been little fresh speculation since and the improved situation on the pitch has, to some extent, diverted attention. It was about time: Milan’s £210m summer outlay, brought about by a level of financial commitment from Li that took many by surprise given the €300m loan he had taken out to expedite the takeover, was designed to restore the club’s old sense of glamour, bringing trophies with it. By late November they were floundering in the bottom half of Serie A under Vincenzo Montella’s doomed management and, with unease growing about Li’s ability to honour his side of the financial bargain, the project smelled – at best – of bread and circuses.

Hiring a club legend in Gattuso was a masterstroke rather than the publicity stunt it could have appeared. This was no case of an entitled ex-pro being parachuted straight into the top level; Gattuso had done his time in spells with Sion, Palermo, OFI Crete and Pisa before returning to Milan as coach of the primavera (youth) side. “I’m not a great coach,” he said after the cup semi-final. “I’ve had to cut my teeth and learn a lot.” But Milan’s physical performance, in particular, has improved under Gattuso. They have conceded only one second-half goal in 2018 and approach Arsenal feeling upbeat when, two months ago, this would have resembled a broadside of blanks between two sinking ships.

The problem is that nobody can be completely sure Milan, as an entity, are in a fit state to stay afloat. There are suggestions that Li is unable to repay the loan he took out, which was borrowed from the hedge fund Elliott Management at an 11.5% interest rate and must be repaid by this October. The club has, at the least, been pursuing refinancing options. Corriere Della Sera, meanwhile, believes Li’s own capital amounts to only €100m, with the rest of the money used to purchase the club garnered from the loan and offshore funds.

In short, there are far more questions than answers, and Uefa clearly felt that way in December when it rejected Milan’s offer of a voluntary agreement to restructure their finances and stave off any FFP punishment brought on by their extravagant transfer dealings. “There are still uncertainties in relation to the refinancing of loans to be paid back in October 2018 and the financial guarantees provided by the main shareholder,” Uefa’s statement read.

Their next move should be apparent soon. In the meantime Gattuso and his players can lighten the financial burden by defeating Arsenal and edging closer to a Champions League place for next season; the issue at hand, though, is that theirs increasingly resembles a salvage operation rather than a march to glory.