Arsenal’s refusal to sell Alexis Sánchez is rooted in long-term economic factors, as well as sporting ones, with the club convinced it would be more damaging to accept a large fee for him this summer than to risk losing him as a Bosman free agent next summer.

Arsène Wenger spoke again on Tuesday about how Sánchez, who has entered the final year of his contract and has made it clear he will not sign a new one, would not be allowed to leave. The Chile forward is a prime target for Manchester City and Paris Saint-Germain, with his desire being to join the former.

“The decision has been made and we will stick to that,” Arsenal’s manager said, from their pre-season tour of China. “The decision is not to sell.”

The club’s dilemma has often been painted in black-and-white terms. Either they sell now for £50m, which is the figure that Sánchez’s suitors could reasonably expect to pay, or they get nothing for him next summer. Yet there are many layers to the situation and one of the most significant concerns Champions League revenue, which Arsenal will miss out on this season, after their fifth-placed Premier League finish, and do not want to miss out on again.

The Champions League is worth roughly £40m per year to the club and, with Sánchez playing alongside the new £53m signing, Alexandre Lacazette, they would be hopeful of making it back into the group phase of the competition. Without him the probability would drop, increasing the likelihood of a hole in the finances.

Moreover, there is an awareness at Arsenal of how Manchester United, for example, were forced – during their recent seasons outside the Champions League – to pay inflated salaries in order to secure A-list signings. The longer a club spends outside Europe’s elite competition, the more such hidden costs rise.

Arsenal are confident their absence from the Champions League will be a one-off. In financial terms it needs to be because the difference between being in or out not only affects player recruitment but sponsorship deals too. Arsenal’s kit contract with Puma expires in 2019. The terms of the renegotiation will be determined, in part, by the club’s Champions League status.

PSG have been back in touch with Arsenal over Sánchez but the London club are far from convinced that City are completely serious about signing him. To do so, they would have to make an offer that brooked no argument – the sort that they made to get the right-back, Kyle Walker, from Tottenham Hotspur, or United did for the striker, Romelu Lukaku, from Everton. Sánchez’s contractual position makes such comparisons more difficult but Arsenal have little evidence that City are prepared to move strongly for their player.

Arsenal’s stance is categoric and it is reinforced by the knowledge that it would be fiendishly difficult to sign a replacement for Sánchez – even for £50m. They have looked and shuddered at the nine-figure sums being bandied about for Monaco’s Kylian Mbappé or the €140m price tag that Juventus have put on Paulo Dybala. Wenger wants the Monaco winger Thomas Lemar but the French club believe that he is worth €80m. In other words, a deal looks problematic.

Arsenal have told Sánchez that they expect him to honour the final year of his contract and nobody at the club is worried about him reapplying himself on 1 September, if he has been unable to force a move. In terms of dressing-room morale, the effect of losing the team’s talisman is another vital consideration and, with the arguments raging, Arsenal believe that theirs are the most compelling.