Arsène Wenger says he has made a financial “sacrifice” in deciding to risk losing Alexis Sánchez on a free transfer next summer, with Arsenal’s sporting prospects coming ahead of any off-pitch concerns.

Sánchez is likely to depart without a fee unless a new contract is agreed with the club – a situation that Wenger said has not progressed. There has been interest in the forward from a number of other clubs in pre-season but the Arsenal manager has weighed up the pros and cons of retaining him and resolved that the football benefits he brings outweigh any potential transfer fee.

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“At the moment no, because we have not progressed on that front,” Wenger said when asked whether Sánchez will sign a new deal. “He is a player who goes into the final year of his contract and prepares for the season.”

Pressed on whether that means he is willing to let the Chile international depart for nothing, Wenger continued: “That is a consequence of what I say, yes, unfortunately. But we have to make a choice between efficiency on the field and financial interest, and most of the time if you can find a good compromise it’s better. But in this case, I think I prioritise the fact that he will be useful on the sporting side.”

He said it was not a perfect state of affairs but left the door open for Sánchez to sign a contract that has been on the table since last season.

“Look, let’s not be wrong, it’s not an ideal situation on the financial side and it demands some sacrifice,” he said. “But first of all it doesn’t mean the players who are in the final year of their contract will not extend their contract. You have still that possibility and we work on that as well.”

Wenger, who also explained that he supports the proposed early closure of future Premier League transfer windows, underlined that the decision not to let Sánchez leave was taken by him rather than Arsenal’s board. “It’s my decision, but after the board has to, of course, agree with me,” he said. “And if they don’t agree we have to consider it as well, and I will accept it. But the board is behind me on that.”

He accepted, though, that the potential gains and losses involved with keeping Sánchez are impossible to calculate precisely and that such situations tend to be unique to the club in question.

“You cannot,” he said. “You can have an estimation of what it costs if you lose the player, what it costs if you extend the player [’s contract], what it costs if you buy a new player. You can do that, approximately. After that, the ratio between what the player will cost and what he brings back, this has gone.

“How can you quantify today what Neymar costs? Will he bring €300m back [to Paris Saint-Germain]? It’s impossible to say. There is a part that is rational, and the other part is completely irrational: it is passion, ego, pride, you can call that how you want. How much is that worth financially? Maybe that’s down to every club.”

Mesut Özil will also be out of contract at the end of the season, and Wenger said he remains “optimistic” that both he and Sánchez will eventually agree new terms – implying that this may be easier to arrange if the team is performing well.

“Look, both players are happy at the club,” he said. “So, for me, after that you have to meet their needs. Their needs are their desire for success and their needs are as well financial. I think if we can meet their needs on the pitch, there is more chance to extend their contracts.”

Alex Oxlade-Chamberlain is another player to have been linked with a move away from Arsenal but Wenger expects the midfielder to join Sánchez and Özil in remaining at the club, although he said “100% [certainty] in our job never exists” when asked whether all three would definitely stay.

Wenger also confirmed he wants midfielder Jack Wilshere, who is returning to fitness after a leg fracture, to stay at Arsenal this season.